Andrés F. Reyes Lega

Andrés F. Reyes Lega
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Andrés F. verified their affiliation via an institutional email.
Los Andes University (Colombia) | UNIANDES · Department of Physics

Ph.D.

About

50
Publications
7,263
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279
Citations
Additional affiliations
December 2011 - March 2012
Institute of Mathematical Sciences
Position
  • Visiting Scientist
March 1997 - September 1999
Los Andes University (Colombia)
Position
  • Research Assistant
January 2010 - present
Universidad de los Andes
Position
  • Professor (Associate)

Publications

Publications (50)
Article
Full-text available
It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons, or distinguishable particles...
Article
Full-text available
We consider the dynamics of the Sorkin-Johnston (SJ) state for a massless scalar field in two dimensions. We conduct a study of the renormalized stress-tensor by a subtraction procedure, and compare the results with those of the conformal vacuum, with an important contribution from correction term. We find a large trace anomaly and compute backreac...
Article
Full-text available
Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain "doubling" of the Hilbert space. In this work we show that this redundancy in the Hilbert space can be completely lifted if the relevant ort...
Preprint
Full-text available
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This,...
Article
Full-text available
We use infinite dimensional self-dual \(\mathrm {CAR}\) \(C^{*}\)-algebras to study a \({\mathbb {Z}}_{2}\)-index, which classifies free-fermion systems embedded on \({\mathbb {Z}}^{d}\) disordered lattices. Combes–Thomas estimates are pivotal to show that the \({\mathbb {Z}}_{2}\)-index is uniform with respect to the size of the system. We additio...
Article
An approach to renormalization of scalar fields on the Doplicher–Fredenhagen–Roberts (DFR) quantum spacetime is presented. The effective nonlocal theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singulari...
Chapter
Full-text available
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a C*-algebra, one can construct a density operator describing the state in the GNS representation space. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambiguit...
Preprint
Full-text available
An approach to renormalization of scalar fields on the Doplicher-Fredenhagen-Roberts (DFR) quantum spacetime is presented. The effective non-local theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singular...
Preprint
Full-text available
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambig...
Article
Full-text available
We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analog of such operators. We then study the algebra of these ope...
Article
Full-text available
Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in the [Formula: see text] lattice, we depart from the well-known Araki–Evans [Formula: see text] index for quasi-free fermion states and rewrite it in terms of states rather than in terms of basis projections. Furthermore, we reformulate results that relate eq...
Article
Full-text available
The observables associated with a quantum system S form a non-commutative algebra A S . It is assumed that a density matrix ρ can be determined from the expectation values of observables. But A S admits inner automorphisms a→uau ⁻¹ , a, u ∈ A S , u*u = uu* = 1, so that its individual elements can be identified only up to unitary transformations. So...
Preprint
Full-text available
Within the setting of infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras describing fermions in the $\mathbb{Z}^{d}$-lattice, we depart from the well-known Araki-Evans $\sigma(P_{1},P_{2})$ $\mathbb{Z}_{2}$-index for quasi-free fermion states and rewrite it in terms of states, rather than in terms of basis projections. Furthermore, we r...
Preprint
Full-text available
We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analogue of such operators. We then study the algebra of these o...
Preprint
Full-text available
The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $\rho$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner automorphisms $a\mapsto uau^{-1},\; a,u\in {\mathcal A}_S$, $u^*u=u^*u=1$, so that its individual elements can...
Preprint
We use infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras to study the existence of a $\mathbb{Z}_{2}$-index, which classifies free-fermions systems embedded on $\mathbb{Z}^{d}$ disordered lattices. Combes-Thomas estimates are pivotal to show that the $\mathbb{Z}_{2}$-index is uniform with respect to the size of the system. We additiona...
Article
Full-text available
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This,...
Chapter
Full-text available
The Gauss law Balachandran, A. P. a basic role in gauge theories, enforcing gauge invariance Reyes-Lega, A. F. creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear G/H models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with SU...
Preprint
Full-text available
The Gauss law plays a basic role in gauge theories, enforcing gauge invariance and creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear $G/H$ models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with $SU(3)$ of colour which is s...
Preprint
Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain "doubling" of the Hilbert space. In this work we show that this redundancy in the Hilbert space can be completely lifted if the relevant ort...
Chapter
This chapter provides the reader with a general overview of the various topics discussed in this volume, emphasizing the deep relations existing between them. Following a brief historical account of the emergence of the concept of “quantization” both in physics and mathematics, a description of the main concepts and tools appearing in subsequent ch...
Chapter
These notes present an overview of the lectures held by Abhay Ashtekar on the theory of quantum fields in curved space-times and its applications to cosmology at the Summer School “Geometric, topological, and algebraic methods for quantum field theory”, held at Villa de Leyva in 2015. The first part of the notes is pretty much self contained, assum...
Book
Full-text available
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other...
Preprint
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics. Aspects of the representation theory of C*-algebras will be motivated and illustrated in physical terms. Particular...
Conference Paper
Full-text available
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics. Aspects of the representation theory of C*-algebras will be motivated and illustrated in physical terms. Particular...
Chapter
Full-text available
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics. Aspects of the representation theory of C*-algebras will be motivated and illustrated in physical terms. Particular...
Article
Full-text available
A partir de la estrategia reube (Renovación de la Enseñanza Universitaria Basada en Evidencias), abordamos la problemática de la renovación didáctica del proceso de enseñanza/aprendizaje de la docencia universitaria de Física de pregrado. La estrategia de acompañamiento e innovación pedagógica reube se basa en la recolección de evidencias puntuales...
Article
Full-text available
Based on the REBUT (Renovation of Evidence-Based University Teaching) strategy, this paper addresses the didactic problem of the educational renewal of teaching/learning regarding university teaching staff for undergraduate physics programs. The support strategy and pedagogical innovation of REBUT is based on the collection of evidence on the speci...
Book
Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory me...
Book
Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory me...
Article
We have developed a novel approach to entanglement, suitable to be used in general quantum systems and specially in systems of identical particles. The approach is based on the GNS construction of representation of C -algebra of observables. In particular, the notion of partial trace is replaced by the more general notion of restriction of a state...
Preprint
It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons or distinguishable particles....
Article
Full-text available
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation space of the observable algebra, once a state is chosen. In this approach, which is based on the Gelfand-Naimark-S...
Article
Full-text available
A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from pure ones based on taking partial traces is replaced by the more general notion of the restriction of a state to...
Article
Full-text available
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent geometric properties of such systems in algebraic terms. As an application, the problem of quantum indistinguisha...
Article
Full-text available
The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham’s Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connecti...
Article
Full-text available
Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support for this approach. In our work, a geometric approach to quantum indistinguishability is introduced wh...
Article
Full-text available
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum operators are the quantum version of Poincare's vector, i.e., the physically correct angular momentum operato...
Article
Full-text available
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general. It is Wigner’s theorem which allows the u...
Article
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry c...
Chapter
Full-text available
We present results on both the intensity and phase-dynamics of the transient non-linear optical response of a single quantum dot (SQD) with and without the presence of a magnetic field. The time evolution of the Four Wave Mixing (FWM) signal on a sub-picosecond time scale is calculated, taking into account exciton-exciton correlations. The two case...
Article
Full-text available
In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space Q of indistinguishable particles. Following an approach proposed by one of the authors, wave functions are regarded as elements of suitable projective modules over C(Q). We take furthermore into account the G-Theory point of view, where the ro...
Article
Full-text available
We present results on both the intensity and phase-dynamics of the transient non-linear optical response of a single quantum dot (SQD). The time evolution of the Four Wave Mixing (FWM) signal on a subpicosecond time scale is dominated by biexciton effects. In particular, for the cross-polarized excitation case a biexciton bound state is found. In t...
Article
Full-text available
A short survey of the theory of the Quantum Hall effect is given emphasizing topological aspects of the quantization of the conductivity and showing how topological invariants can be derived from the hamiltonian. We express these invariants in terms of Chern numbers and show in precise mathematical terms how this relates to the Kubo formula.
Article
Ultrafast spectroscopy experiments on single quantum dot (SQD) in magnetic fields provide a variety of unexpected results, one of them being the recently reported entanglement of exciton states. In order to explore the entanglement robustness, dephasing mechanisms must be considered. By calculating the non-linear time resolved optical spectrum of a...
Article
Recent experimental results demonstrate an exceptionally high level of control of excitons in a single quantum dot. We report on theoretical results about non-linear optical effects due to exciton-exciton correlations. Our formalism allows us to consider the fully degenerate non-linear spectrum (two laser excitations at the same frequency) as well...
Article
Full-text available
The energy and wavefunction of a quasi-two-dimensional magnetic polaron in semimagnetic semiconductors are calculated by solving a non-linear Wannier equation. A self-consistent solution is presented including exactly the structure factor of the system. We found that the magnetic polaron energy is strongly dependent on temperature and well width. G...
Article
Full-text available
A partir de la estrategia REUBE (Renovación de la Enseñanza UniversitariaBasada en Evidencias), abordamos la problemática de la renovación didácticadel proceso de enseñanza/aprendizaje de la docencia universitariade Física de pregrado. La estrategia de acompañamiento e innovaciónpedagógica REUBE se basa en la recolección de evidencias puntuales sob...

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