Byron Droguett

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• Professor (Assistant) at University of Antofagasta

We compute the one-loop effective action of the Hořava theory, in its nonpro-jectable formulation. The quantization is performed in the Batalin-Fradkin-Vilkovisky formalism. It includes the second-class constraints and the appropriate gauge-fixing condition. The ghost fields associated with the second-class constraints can be used to get the integr...

We investigate the static solutions with rotational symmetry in the nonprojectable Ho\v{r}ava theory in 2+1 dimensions. We consider all inequivalent terms of the effective theory, including the cosmological constant. We find two distinct types of solutions: the first one corresponds to a Lifshitz solution, while the second one is obtained through a...

Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed differential equations. We derive their characteristic equations and solve them using the Laplace transform. We derive...

The main objective of this research work was to investigate the learning of a certain homogeneous reducible differential equation by means of ChatGpt in engineering students, during the second semester of 2024 in Antofagasta-Chile. This research followed a qualitative case study approach. Four students of the differential equations course were chos...

A new approximation function is introduced to fit the solution of a fractional differential equation of order one-half. The analyzed case includes a nonhomogeneous term defined by a modified Bessel function of the first kind. The analytical solution of this equation corresponds to the product of two modified Bessel functions. The new fitting functi...

We investigate the Casimir effect for parallel plates within the framework of Ho\v{r}ava-Lifshitz theory in $3+1$ dimensions, considering the effects of roughness, anisotropic scaling factor, and an uniform constant magnetic field. Quantum fluctuations are induced by an anisotropic charged-scalar quantum field subject to Dirichlet boundary conditio...

This paper presents the integration of GeoGebra applets and ChatGPT artificial intelligence in the learning of exact differential equations in the university context. GeoGebra has established itself as a powerful tool in teaching mathematical concepts, thanks to its ability to dynamically visualize and model, which facilitates deeper understanding...

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutio...

This paper unifies the advantages of combining GeoGebra applets and Gemini AI to enhance mathematics learning for university students, specifically in the differential equations course at the University of Antofagasta, Chile. This combination of technological tools offers an innovative and effective approach to solving separable differential equati...

We present the proof of renormalization of the Hořava theory in the nonprojectable version. We obtain a form of the quantum action that exhibits a manifest Becchi-Rouet-Stora-Tyutin–symmetry structure. Previous analysis has shown that the divergences produced by irregular loops cancel completely between them. The remaining divergences are local. Th...

In this paper, we explore the Casimir effect of a rough membrane within the framework of theories that break Lorentz symmetry. We consider two constant aether vectors: one time-like and other space-like, simultaneously. We employ an appropriate change of coordinates such that the membrane assumes a completely flat border and the remaining terms ass...

Our paper introduces a new theory called Fractional Einstein-Gauss-Bonnet scalar field cosmology, which has significant implications for Cosmology. We derived a modified Friedmann equation and a modified Klein-Gordon equation using fractional calculus to modify the gravitational action integral. Our research reveals non-trivial solutions associated...

We present the proof of renormalization of the Hořava theory, in the nonprojectable version. We obtain a form of the quantum action that exhibits a manifest BRST-symmetry structure. Previous analysis have shown that the divergences produced by irregular loops cancel completely between them. The remaining divergences are local. The renormalization i...

We explore the Casimir effect of a rough membrane within the framework of theories that break Lorentz symmetry. We consider two constant Aether vectors: one timelike and other spacelike, simultaneously. We employ an appropriate change of coordinates such that the membrane assumes a completely flat border and the remaining terms associated with the...

We compute the one-loop effective action of the Hořava theory, in its nonprojectable formulation. We take the quantization of the (2+1)-dimensional theory in the Batalin-Fradkin-Vilkovisky formalism, and comment on the extension to the (3+1) case. The second-class constraints and the appropriate gauge-fixing condition are included in the quantizati...

We investigate the Casimir effect of a rough membrane within the framework of the Hořava–Lifshitz theory in \(2+1\) dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associ...

We investigate the Casimir eect of a rough membrane within the framework of the Hořava-Lifshitz theory in 2 + 1 dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associate...

We perform the Batalin-Fradkin-Vilkovisky quantization of the anisotropic conformal Hořava theory in d spatial dimensions. We introduce a model with a conformal potential suitable for any dimension. We define an anisotropic and local gauge-fixing condition that accounts for the spatial diffeomorphisms and the anisotropic Weyl transformations. We sh...

We perform the Batalin-Fradkin-Vilkovisky quantization of the anisotropic conformal Horava theory in d spatial dimensions. We introduce a model with a conformal potential suitable for any dimension. We define an anisotropic and local gauge-fixing condition that accounts for the spatial diffeomorphisms and the anisotropic Weyl transformations. We sh...

We present an analysis on the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations of the Hořava theory under the Batalin-Fradkin-Vilkovisky quantization, both in the nonprojectable and projectable cases. We obtain that the BRST transformations are intimately related to a particular spatial diffeomorphism along one of the ghost vector fields....

We study the Casimir effect of a membrane embedded in 2+1 dimensions flat cone generated by a massive particle located at the origin of the coordinate system. The flat cone is an exact solution of the nonprojectable Horava theory, similar to general relativity. We consider a scalar field satisfying Dirichlet boundary conditions, and regularize the...

We present an analysis on the BRST symmetry transformations of the Horava theory under the BFV quantization, both in the nonprojectable and projectable cases. We obtain that the BRST transformations are intimately related to a particular spatial diffeomorphism along one of the ghost vector fields. We show explicitly the invariance of the quantum ac...

We perform an analysis of the ultraviolet divergences of the quantum nonprojectable Hořava gravity. We work the quantum-field theory directly in the Hamiltonian formalism provided by the Batalin-Fradkin-Vilkovisky quantization. In this way the second-class constraints can be incorporated into the quantization. A known local gauge-fixing condition l...

We perform an analysis of the ultraviolet divergences of the quantum non-projectable Hořava gravity. We work the quantum field theory directly in the Hamiltonian formalism provided by the Batalin-Fradkin-Vilkovisky quantization. In this way the second-class constraints can be incorporated to the quantization. A known local gauge-fixing condition le...

We perform the Batalin-Fradkin-Vilkovisky (BFV) quantization of the 2+1 projectable and the 3+1 nonprojectable versions of the Hořava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the integration on canonical momenta reproduces the quantum Lagrangian known from the proof...

We perform the BFV quantization of the 2+1 projectable and the 3+1 nonprojectable versions of the Horava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the integration on canonical momenta reproduces the quantum Lagrangian known from the proof of renormalization of Barvins...

We show that the Batalin-Fradkin-Vilkovisky (BFV) quantization scheme can be implemented in the nonprojectable (2+1)-Hořava theory. This opens the possibility of imposing more general gauge conditions in the quantization of this theory. The BFV quantization is based on the canonical formalism, which is suitable to incorporate the measure associated...

We show that the BFV quantization scheme can be implemented in the nonprojectable 2+1 Horava theory. This opens the possibility of imposing more general gauge conditions in the quantization of this theory. The BFV quantization is based on the canonical formalism, which is suitable to incorporate the measure associated to the second-class constraint...

The Hořava theory in 2+1 dimensions can be formulated at a critical point in the space of coupling constants where it has no local degrees of freedom. This suggests that this critical case could share many features with 2+1 general relativity, in particular its large-distance effective action that is of second order in derivatives. To deepen on thi...

The Horava theory in 2+1 dimensions can be formulated at a critical point in the space of coupling constants where it has no local degrees of freedom. This suggests that this critical case could share many features with 2+1 general relativity, in particular its large-distance effective action that is of second order in derivatives. To deepen on thi...

We present the interesting case of the 2+1 nonprojectable Horava theory formulated at the critical point, where it does not posses local degrees of freedom. The critical point is defined by the value of a coupling constant of the theory. We discuss how, in spite of the absence of degrees of freedom, the theory admits solutions with nonflat or nonco...

We present the quantization of the 2+1 dimensional nonprojectable Hořava theory. The central point of the approach is that this is a theory with second-class constraints, hence the quantization procedure must take account of them. We consider all the terms in the Lagrangian that are compatible with the foliation-preserving-diffeomorphisms symmetry,...

We present the quantization of the 2+1 dimensional nonprojectable Horava theory. The central point of the approach is that this is a theory with second-class constraints, the quantization procedure must take account of them. We consider all the terms in the Lagrangian that are compatible with the foliation-preserving-diffeomorphisms symmetry, up to...

We show that the solution corresponding to the gravitational field of a point particle at rest in 2+1 nonprojectable Hořava is exactly the same as 2+1 general relativity with the same source. In general relativity this solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system...

We show that the solution corresponding to the gravitational field of a point particle at rest in 2+1 nonprojectable Horava is exactly the same as its analogous in 2+1 General Relativity. This solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system we couple the Horava theor...

We contrast the dynamics of the Hořava theory with anisotropic Weyl symmetry with the case where this symmetry is explicitly broken, which is called the kinetic-conformal Hořava theory. To do so, we perform the canonical formulation of the anisotropic conformal theory at the classical level with a general conformal potential. Both theories have the...

We perform the canonical formulation of the conformal Horava theory at the classical level. The conformal symmetry is anisotropic in the sense that the lapse function transform with a weight different to the spatial metric. The conformal theory shares some similarities with the the kinetic-conformal theory that has been studied previously. The diff...

We compute the Casimir energy which arises in a bi-dimensional surface due to the quantum fluctuations of a scalar field. We assume that the boundaries are non-flat and the field obeys Dirichlet condition. We re-parametrize the problem to one which has flat boundary conditions and the irregularity is treated as a perturbation in the Laplace–Beltram...

We compute the Casimir energy which arises in a bi-dimensional surface due to the quantum fluctuations of a scalar field. We assume that the boundaries are irregular and the field obeys Dirichlet condition. We re-parametrize the problem to one which has flat boundary conditions and the irregularity is treated as a perturbation in the Laplace-Beltra...

This work deals with thermo-statistical approaches for describing phenomenon of gravitational clustering in cosmology. We have introduced a family of N-body Hamiltonian toy models that describe self-gravitating gas embedded on a n-sphere Sn within a n+1-dimensional real space Rn+1. The closed character of these Riemannian manifolds avoids the incid...