Giuseppe Vitiello

Giuseppe Vitiello
University of Salerno | UNISA · Department of Physics "E. R. Caianiello" DF

Honorary Professor, Ph.D. in Physics

About

392
Publications
115,404
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8,663
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Introduction
Giuseppe Vitiello currently works at the Department of Physics "E. R. Caianiello", Università degli Studi di Salerno. Giuseppe does research in Elementary Particle Physics, Mathematical Physics, Quantum Field Theory, and the physics of biological systems and brain studies. One of his current projects is 'Linguistics and some aspects of its underlying dynamics: suggestions from Quantum Field Theory'.
Additional affiliations
November 1974 - present
University of Salerno
Position
  • Professor
January 1980 - December 2018
INFN - Istituto Nazionale di Fisica Nucleare
Position
  • Researcher
Education
January 1972 - December 1974
November 1964 - July 1970

Publications

Publications (392)
Book
Full-text available
"Il cervello è come un'orchestra. Meglio ancora, come un gruppo jazz che non ha bisogno di un direttore d'orchestra. Ogni neurone vive in un campo che ascolta, al quale si adatta e contribuisce, fuso nell'unità di suono e ritmo. Globale e istantaneo." La teoria quantistica dei campi applicata allo studio del cervello mostra che l’attività simultan...
Article
Full-text available
The asymmetry between the left and right sides seems to be a general principle of organization of the nervous systems in Bilateria, providing the foundations for a plethora of leftward and rightward biases in behaviour as documented in species ranging from Caenorhabditis elegans nematodes to humans. Several theories have been put forward to account...
Preprint
Full-text available
Magnetic fluids, commonly called ferrofluids, are excellent candidates for several important research fields, including computation, energy harvesting, biomedical applications, soft robotics, and exploration. Our study presents a groundbreaking discovery of significant phase correlations between two separate samples of ferrofluid, even when they ar...
Chapter
In this paper we analyse the conditions for attributing to AI autonomous systems the ontological status of “artificial moral agents”, in the context of the “distributed responsibility” between humans and machines in Machine Ethics (ME). In order to address the fundamental issue in ME of the unavoidable “opacity” of their decisions with ethical/lega...
Article
Full-text available
We discuss the asymmetries of dynamical origin that are relevant to functional brain activity. The brain is permanently open to its environment, and its dissipative dynamics is characterized indeed by the asymmetries under time translation transformations and time-reversal transformations, which manifest themselves in the irreversible “arrow of tim...
Preprint
Regular light-dark cycles greatly affect organisms, and events like eclipses induce distinctive physiological and behavioural shifts. While well-documented in animals, plant behaviour during eclipses remains largely unexplored. Here we monitored multiple spruce trees to assess their individual and collective bioelectrical responses to a solar eclip...
Preprint
Full-text available
Bayes’ theorem is shown to be implicit in the quantum formalism describing the entanglement between an open system X and its thermal bath Y . The formalism adopted here is the Thermo Field Dynamics in quantum field theory at finite temperature. Bayes’ theorem turns out to be naturally related to the minimization of free energy of the system. A disc...
Article
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The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representatio...
Article
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The in situ measurement of the bioelectric potential in xilematic and floematic superior plants reveals valuable insights into the biological activity of these organisms, including their responses to lunar and solar cycles and collective behaviour. This paper reports on the “Cyberforest Experiment” conducted in the open-air Paneveggio forest in Val...
Article
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Trees employ impulses of electrical activity to coordinate actions of their bodies and long-distance communication. There are indications that the vascular system might act as a network of pathways for traveling electrical impulses. A question arises about the correlation and interplay between the molecular (microscopic) level and the macroscopic o...
Article
Full-text available
We review processes by which different sounds, such as meditation music, mantra, kindness, or hatred expressions, and noises induce responses from cells and their components. We define ‘good’ or ‘bad’ sounds as those enhancing or inhibiting the cell’s biological activity, respectively. It is highlighted that the cellular dynamics results in a coher...
Article
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The mechanism of spontaneous breakdown of symmetry in quantum field theory is reviewed, the Goldstone theorem derived and the formation of ordered patterns is discussed. Metamorphoses and fractal self-similarity are described in terms of the dynamical rearrangement of symmetry in spontaneously broken symmetry theories. The isomorphism between fract...
Presentation
Full-text available
Experimental observations and theoretical modeling on the effects of sounds on cells. . Dal Lin, C.; Brugnolo, L.; Marinova, M.; Plebani, M.; Iliceto, S.; Tona, F.; Vitiello, G. Toward a Unified View of Cognitive and Biochemical Activity: Meditation and Linguistic Self-Reconstructing May Lead to Inflammation and Oxidative Stress Improvement. Entrop...
Article
Full-text available
In this view point paper, we briefly summarize some of the clinical, biochemical and biophysical results obtained in our research on Relaxation Response. We also qualitatively describe the theoretical biophysical model that could link them. Our work points to a unified view of the human biological system activity, joining the dynamics ruling the in...
Preprint
Electrical activity is used by plants in long term signalling and information transfer between the distant parts of the plant. Biopotential recordings from trees in a natural environment have been so far less discussed in scientific literature. Here we present our data about the open science experiment TRee-hUMAn iNterface (TRUMAN) located in Panev...
Preprint
Full-text available
Electrical activity is used by plants in long term signalling and information transfer between the distant parts of the plant. Biopotential recordings from trees in a natural environment have been so far less discussed in scientific literature. Here we present our data about the open science experiment TRee-hUMAn iNterface (TRUMAN) located in Panev...
Chapter
The activity of the neocortex presents the formation of extended configurations of oscillatory motions modulated in amplitude and phase and involving myriads of neurons. As observed by Lashley, nerve impulses are transmitted from cell to cell through defined cell connections. However, all behavior seems to be determined by masses of excitations, wi...
Article
Full-text available
We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits to give a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula which...
Preprint
Full-text available
We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits to give a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula which...
Conference Paper
Full-text available
In the actual panorama of machine learning (ML) algorithms, the issue of the real-time information extraction/classification/manipulation/analysis of data streams (DS) is acquiring an ever-growing relevance. They arrive generally at high speed and always require an unsupervised real-time analysis for individuating long-range and higher order correl...
Article
Full-text available
Background and aim: Mental stress represents a pivotal factor in cardiovascular diseases. The mechanism by which stress produces its deleterious ischemic effects is still under study but some of the most explored pathways are inflammation, endothelial function and balancing of the thrombotic state. In this scenario, von Willebrand factor (vWF) is...
Chapter
I review one of the papers by Eliano Pessa and myself where we model neural networks as many-body systems. The mathematical formalism underlying the model is here presented. The information input induces the spontaneous breakdown of the SU(2) symmetry of the units of the neural net. The order parameter describes the collective correlation modes pro...
Article
Full-text available
A horizontal electrohydrodynamic (EHD) liquid bridge (also known as a “floating water bridge”) is a phenomenon that forms when high voltage DC (kV·cm−1) is applied to pure water in two separate beakers. The bridge, a free-floating connection between the beakers, acts as a cylindrical lens and refracts light. Using an interferometric set-up with a l...
Article
Full-text available
This is a perspective on some theoretical studies obtained in the framework of the dissipative quantum model of brain. The formation of long range neuronal correlations is described in terms of quantum field theory mechanisms operating in systems with a huge number of degrees of freedom. Memory states are constructed through the condensation in the...
Article
Full-text available
Mechanical vibrations seem to affect the behaviour of different cell types and the functions of different organs. Pressure waves, including acoustic waves (sounds), could affect cytoskeletal molecules via coherent changes in their spatial organization and mechano-transduction signalling. We analyzed the sounds spectra and their fractal features. Ca...
Article
Full-text available
Stress appears to be the basis of many diseases, especially myocardial infarction. Events are not objectively “stressful” but what is central is how the individual structures the experience he is facing: the thoughts he produces about an event put him under stress. This cognitive process could be revealed by language (words and structure). We follo...
Article
Full-text available
In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The coherence of th...
Preprint
Full-text available
In our recent works we reported that physical and chemical characteristics of serum can vary in relation to the psychic activity of an individual depending on whether it is oriented to stress or relaxation. We wandered if these observations could be accompanied by an appreciable modification of the Ph, electric conductivity and Delayed Luminescence...
Preprint
Full-text available
Convincing evidence has documented that mechanical vibrations profoundly affect the behaviour of different cell types and even the functions of different organs. Pressure waves such as those of sound could affect cytoskeletal molecules with coherent changes in their spatial organization and are conveyed to cellular nucleus via mechanotransduction....
Article
A brief review of our previously introduced forward and backward in time formalism for non-relativistic electron diffraction and its relativistic extension to study photons in time and space is presented. The zero-point energy in the Planck black body spectrum emerges naturally once time-symmetric motion — inherent in Maxwell equations — is invoked...
Article
The study of the damped harmonic oscillator shows that dissipation could be seen at the origin of the zero point energy, which is the signature of quantum behavior. This is in accord with ’t Hooft proposal that loss of information in a completely deterministic dynamics would play a rôle in the quantum mechanical nature of our world. We show the equ...
Chapter
Full-text available
A significant chapter of the short history of formal philosophy is related with the notion and the theory of the so-called “Social Welfare Functions (SWFs)”, as a substantial component of the “social choice theory”. One of the main uses of SWFs is aimed, indeed, at representing coherent patterns (effectively, algebraic structures of relations) of i...
Article
Full-text available
An earlier forward and backward in time formalism developed by us to discuss non-relativistic electron diffraction is generalized to the relativistic case and here applied to photons. We show how naturally the zero-point energy emerges in the Planck black-body spectrum once symmetric in time motion—inherent in the Maxwell equations—is invoked for p...
Chapter
The emergence of collective behavior of myriads of neurons forming coherent patterns of amplitude modulated oscillations is described in terms of quantum field theory formalism with spontaneous breakdown of symmetry. The dissipative quantum model of brain and its results in agreement with observations are discussed. Mental activity and brain activi...
Article
Full-text available
We study the molecular dynamics underlying the formation and the evolution of hurricanes. The giant global structure of hurricanes cannot be solely the results of random molecular kinematics. We show that the non-stationary, topologically non-trivial hurricane behavior is the manifestation of the collective dynamics at the molecular level. This is...
Article
Full-text available
In this paper we discuss the ontology of flavor states of oscillating neutrinos. While an heuristic approach to this subject, experimentally successful in the high energy regime, is generally adopted, a logically consistent definition of flavor states describing neutrinos produced and detected in weak processes is still desirable and essential from...
Article
Full-text available
The entanglement phenomenon plays a central role in quantum optics and in basic aspects of quantum mechanics and quantum field theory. We review the dissipative quantum model of brain and the role of the entanglement in the brain-mind activity correlation and in the formation of assemblies of coherently-oscillating neurons, which are observed to ap...
Article
In this work we expand on findings previously reported [Wexler et al., PCCP, 2016, 18, 16281] on the experimental observation of a phase transition in a hydrogen bonded liquid manifesting in long range dipole-dipole interactions. The studied system, liquid water stressed by an electric field, exhibits collective oscillations brought about through s...
Article
In this paper, I focus on a couple of features of quantum field theory commenting briefly on how they have been emerging also as key aspects in brain studies. In particular, I comment on the relation between brain functional activity and mind (mental activity). The role played by the doubling of the system degrees of freedom (the Double) is conside...
Book
Full-text available
IT: Emilio Del Giudice era persona di grande cultura e di molte letture, dagli interessi più vari e proprio per questo quando parlava o scriveva desiderava essere compreso il più possibile da chiunque fosse interessato ad ascoltarlo. Nella scelta degli scritti proposti, si è cercato di includere gli argomenti che più l’hanno appassionato: politica,...
Preprint
Full-text available
In this paper we discuss the ontology of flavor states of oscillating neutrinos. While an heuristic approach to this subject, experimentally successful in the high energy regime, is generally adopted, a logically consistent definition of flavor states describing neutrinos produced and detected in weak processes is still desirable and essential from...
Preprint
Full-text available
In this paper we discuss the ontology of flavor states of oscillating neutrinos. While an heuristic approach to this subject, experimentally successful in the high energy regime, is generally adopted, a logically consistent definition of flavor states describing neutrinos produced and detected in weak processes is still desirable and essential from...
Chapter
In a typical scattering process among elementary particles, observation is limited to the asymptotic regions, where ingoing particles and outgoing particles behave like free, non-interacting particles. The region of interaction is not accessible to our observations. These would be interfering with the phenomenon under study. The interaction region...
Preprint
Full-text available
An earlier forward and backward in time formalism developed by us to discuss non-relativistic electron diffraction is generalized to the relativistic case and here applied to photons. We show how naturally the zero-point energy emerges in the Planck black-body spectrum once symmetric in time motion - inherent in the Maxwell equations - is invoked f...
Article
Water kept in contact with cellulose has not been a “juicy” research topic until now. This is surprising because cellulose is a major component of the cell walls in green plants. It is also a common material used in many artificial systems, e.g., filters. In this work, we review some of our experimental results and show that iteratively bringing ce...
Article
Full-text available
We present here a model of meridians in the formalism of the gauge theory paradigm of quantum field theory with spontaneous breakdown of symmetry. We discuss the origin and dynamic self-focusing propagation of the electromagnetic field in coherent states and the role it plays in our meridian modeling. Within this frame, we consider the formation of...
Preprint
We discuss the role of water bridging the DNA-enzyme interaction by resorting to recent results showing that London dispersion forces between delocalized electrons of base pairs of DNA are responsible for the formation of dipole modes that can be recognized by \textit{Taq} polymerase. We describe the dynamic origin of the high efficiency and precis...
Preprint
Full-text available
By resorting to the Burgers model for hurricanes, we study the molecular motion involved in the hurricane dynamics. We show that the Lagrangian canonical formalism requires the inclusion of the environment degrees of freedom. This also allows the description of the motion of charged particles. In view of the role played by moist convection, cumulus...
Article
Full-text available
We analyze the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a theoretical tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. We feed the values of the experimental paramete...
Article
Full-text available
By resorting to the Burgers model for hurricanes, we study the molecular motion involved in the hurricane dynamics. We show that the Lagrangian canonical formalism requires the inclusion of the environment degrees of freedom. This also allows the description of the motion of charged particles. In view of the role played by moist convection, cumulus...
Article
Full-text available
In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon fields. As a result we obtain that the relation holds which in the...
Preprint
In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon fields. As a result we obtain that the relation holds which in the...
Chapter
The mechanism of the dynamical rearrangement of symmetry in quantum field theory underlies the phenomenon of coherent boson condensation in the vacuum state. Coherent states appear to be related to fractal self-similarity. The dynamical paradigm of coherence opens the way to an integrated vision of natural phenomena and it may possibly rule morphog...
Article
Full-text available
Average evoked potential data recorded as impulse responses of brains to electric shocks show Bessel-like functional distributions which we analyze in terms of couples of damped/amplified oscillators. This reproduces results obtained in terms of ordinary differential equations (Freeman K-sets) and offers the possibility of a direct connection with...
Article
A long history of research has pursued the use of embryonic factors isolated during cell differentiation processes for the express purpose of transforming cancer cells back to healthy phenotypes. Recent results have clarified that the substances present at different stages of cell differentiation-which we call stem cell differentiation stage factor...
Article
Full-text available
By resorting to recent results, we show that an isomorphism exist between linguistic features of the Minimalist Program and the quantum field theory formalism of condensed matter physics. Specific linguistic features which admit a representation in terms of the many-body algebraic formalism are the unconstrained nature of recursive Merge, the opera...
Article
Full-text available
The behavior of thermal vacuum condensates of scalar and fermion fields is analyzed and it is shown that the condensate of Maxwell fields reproduces the characteristics of the cosmic microwave radiation. By studying fermion thermal states with the temperature of the cosmic neutrino background, we derive a value of the sum of the active neutrino mas...
Article
Full-text available
We consider a simple classical model in phase-space resembling the quantum one used for the description of neutrino oscillations and investigate the possibility of defining an analogue to the mixing transformation and to the oscillation formula in terms of generalized coordinates.
Article
Full-text available
We discuss the role of water bridging the DNA-enzyme interaction by resorting to recent results showing that London dispersion forces between delocalized electrons of base pairs of DNA are responsible for the formation of dipole modes that can be recognized by Taq polymerase. We describe the dynamic origin of the high efficiency and precise targeti...
Preprint
Full-text available
We discuss the role of water bridging the DNA-enzyme interaction by resorting to recent 1 results showing that London dispersion forces between delocalized electrons of base pairs of DNA 2 are responsible for the formation of dipole modes that can be recognized by Taq polymerase. 3 We describe the dynamical origin of the high efficiency and precise...
Article
Full-text available
The results of laboratory observations and of theoretical analysis carried on by Walter Freeman and other investigators suggest that the macroscopic functional stability and high efficiency of the brain depend on the coherent oscillations of assemblies of millions of neurons, not solely by the properties of single neurons. The approach focusing on...
Article
Full-text available
In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterize...
Preprint
In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterize...
Chapter
Under the conditions of constant magnetic field and harmonic scalar potential, electrodynamics appears to be isomorph to fractal self-similar structures and squeezed coherent states. Relevance of coherent states and electromagnetic interaction and ubiquity of fractals point to a unified vision of Nature.
Article
Full-text available
We analize the non-cyclic geometric phase for neutrinos propagating in the matter and through a magnetic field. We find that the geometric phase and the total phase associated to the mixing phenomenon and to the neutrino spin rotation can represent a tool to distinguish between Dirac and Majorana neutrinos. Future experiments, based on interferomet...
Preprint
We show that mixing transformations for Dirac fields arise as a consequence of the non-trivial interplay between rotations and Bogoliubov transformations at level of ladder operators. Indeed the non-commutativity between the algebraic generators of such transformations turns out to be responsible of the unitary inequivalence of the flavor and mass...
Article
Full-text available
We show that mixing transformations for Dirac fields arise as a consequence of the non-trivial interplay between rotations and Bogoliubov transformations at level of ladder operators. Indeed the non-commutativity between the algebraic generators of such transformations turns out to be responsible of the unitary inequivalence of the flavor and mass...
Article
Full-text available
In this paper we consider dipole-mediated correlations between DNA and enzymes in the context of their water environment. Such correlations emerge from electric dipole-dipole interactions between aromatic ring structures in DNA and in enzymes, and they are mediated by radiative fields that stimulate transitions between the $l=0$ and $l=1$ rotationa...
Preprint
In this paper we consider dipole-mediated correlations between DNA and enzymes in the context of their water environment. Such correlations emerge from electric dipole-dipole interactions between aromatic ring structures in DNA and in enzymes. We show that there are matching collective modes between DNA and enzyme dipole fields, and that a dynamic...
Preprint
The aim of this paper is the study of thermal vacuum condensate for scalar and fermion fields. We analyze the thermal states at the temperature of the cosmic microwave background (CMB) and we show that the vacuum expectation value of the energy momentum tensor density of photon fields reproduces the energy density and pressure of the CMB. We perfor...
Article
Full-text available
The formalism describing fractal self-similar structures has been shown in recent works to be isomorphic to the one of a system of damped/amplified oscillators, which is a prototype of a dissipative system and of the environment in which it is embedded, and to squeezed coherent states. Fractal-like structures appear to be generated by coherent quan...
Article
Full-text available
Brains acquire knowledge by acting into the environment to confirm or reject hypotheses imagined from memory in the action-perception cycle. Memories are created and updated through phase transitions from a gas-like ground state to a liquid-like condensate that we model as a dissipative quantum field. Each field in the liquid state is based in a su...
Article
Full-text available
The aim of this paper is to study thermal vacuum condensate for scalar and fermion fields. We analyze the thermal states at the temperature of the cosmic microwave background (CMB) and we show that the vacuum expectation value of the energy momentum tensor density of photon fields reproduces the energy density and pressure of the CMB. We perform th...
Article
Brains acquire knowledge by acting into the environment to confirm or reject hypotheses imagined from memory in the actionperception cycle. Memories are created and updated through phase transitions from a gas-like ground state to a liquid-like condensate that we model as a dissipative quantum field. Each retrieved memory is imposed in the amplitud...
Article
The discovery of the Higgs particle and the experimental confirmation of the Higgs mechanism are discussed in the conceptual frame of the elementary particle physics of the past century and of the first decades of the present one. Some of the physical details show that the vision of the world made of elementary constituents, free from any interacti...
Article
Full-text available
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like $B_{s}^{0}-\bar{B}_{s}^{0}$ and the $K^{...
Chapter
We study the energy consumption of the brain in the framework of the dissipative many-body model and the generalized Carnot cycle model. We focus our attention on the expenditure of energy to facilitate the emergence of patterns and dissipation of so-called dark energy in knowledge retrieval. The general picture of the process, by which brains cons...
Chapter
Full-text available
Here the phenomenon of interest is the flash of recognition and accompanying emotion one experiences when one receives a familiar stimulus. We explain the speed and richness of the event by postulating phase transitions in cortical neuropil: condensation from a gas-like phase to a liquid-like phase followed by evaporation. We model the process with...
Article
Full-text available
The Unesco Chair " Anthropology of Health, biosphere and Healing System " inside the University of Genoa (IT) is a unique experience inside the University of Genoa that stems from a cultural necessity to fill and a wealth of knowledge to preserve health, environment and treatment strategies considered strictly connected in modern medicine. This new...
Article
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We find that a geometric phase characterizes the phenomenon of mixing of photons with axion-like particles (ALPs). The laboratory observation of such a phase may provide a novel tool able to detect such a mixing phenomenon. We show that the geometric phase is dependent on the axion-like particle mass and coupling constant. We discuss an interferome...
Article
Full-text available
The system of two damped/amplified oscillator equations is of widespread interest in the study of many physical problems and phenomena, from inflationary models of the Universe to thermal field theories, in condensed matter physics as well in high energy physics, and also in neuroscience. In this report we review the equivalence, in a suitable para...
Article
Full-text available
In our previous work the possibility to use the Aharonov-Anandan invariant as a tool in the analysis of disparate systems has been shown, including Hawking and Unruh effects, as well as graphene physics and thermal states. We show that the vacuum condensation, characterizing such systems, is also related with geometric phases and we analyze the pro...
Article
Full-text available
We show that it is possible to decompose the generator of mixing transformations for Dirac fields, in terms of a rotation and two ordinary Bogoliubov transformations, accounting for mass shift in the fermion fields. This result clarifies the nature of the mechanism which leads to the unitary inequivalence of the flavor and mass vacua.
Article
Full-text available
By resorting to Freeman's observations showing that the distribution functions of impulse responses of cortex to sensory stimuli resemble Bessel functions, we study brain dynamics by considering the equivalence of spherical Bessel equation, in a given parametrization, to two oscillator equations, one damped and one amplified oscillator. The study o...