arXiv subjects

R. Cartas-Fuentevilla

Publications and source records attributed to R. Cartas-Fuentevilla.

At least 19 recordsLinked to original sources

arXiv2026

A hypercomplex partition function for dissipative quantum field theory

We develop a finite-temperature formulation for a hypercomplex dissipative quantum field theory [1], using the imaginary-time path-integral approach and the idempotent structure of the hypercomplex algebra. The resulting partition function naturally separates into two conjugate complex sectors whose recombination preserves the hypercomplex Hermitian structure while generating a nontrivial thermal phase. From this construction, the standard thermodynamic observables are obtained consistently, and the conventional relativistic charged Bose gas is recovered in the vanishing-dissipation limit. Beyond this equilibrium correspondence, the hypercomplex formulation reveals a distinctive perturbative hierarchy: dissipative effects first appear in the complementary phase sector, while corrections to ordinary real thermodynamic quantities arise only at higher order. These results show that dissipation can be encoded through an enlarged algebraic thermal structure without abandoning the familiar framework of relativistic finite-temperature field theory, opening a path toward broader applications of hypercomplex methods in dissipative, open, and effectively non-Hermitian quantum systems.

math-ph↗

arXiv2026

Hypercomplex formulation of dissipative scalar electrodynamics and phase transitions

A hypercomplex formulation of scalar electrodynamics is developed, in which dissipation emerges as an intrinsic dynamic property dictated by the extended local gauge symmetry U(1)XSO(1,1). By constructing an effective free-energy functional, we derive the generalized Ginzburg-Landau equations and analyze the thermodynamic stability of the system. Our analysis of the vacuum state up to the fourth order reveals that the constraint on the coefficients associated with the invariants prohibits the coexistence of mixed states, formally establishing the existence of a bicritical point. Consequently, upon crossing the critical temperature, the system is forced to undergo a discontinuous first-order phase transition. Furthermore, we demonstrate that the hyperbolic symmetry induces a structural instability when the effective quartic couplings take negative values, rendering the free energy unbounded from below and creating asymptotic directions of instability.

hep-th↗

arXiv2026

Hypercomplex Yang-Mills Theory as a Bipartite Gauge Field Model

A non-Abelian gauge field framework is proposed using the hypercomplex ring formalism. This extension generates non-compact hyperbolic symmetries, which, alongside the compact gauge symmetries, double the internal degrees of freedom. This will enable the description of bipartite gauge systems and demonstrate how field dissipation operates at the dynamical level. Working within a commutative ring allows for the decoupling of the algebraic structures and facilitates the construction of solutions to the equations of motion.

hep-th↗

arXiv2024

The propagator field theory revisited: a Lorentz symmetry breaking approach

It is well known that the propagator for a massive scalar field is ill-defined in the coordinate space for $d\geq2$, in particular it diverges at the light-cone; we show that by using Lorentz symmetry breaking weighted measures, an infinite family of propagators can be constructed in an in\-finite\-simal strip near the light-cone, which are labeled by the weight of the measure; hence, the results will provide a finite quantum amplitude for a massive particle for propagating on the light-cone. The propagators regarded as smooth two-points functions, increase within a region smaller than the Compton wavelength, and decrease beyond that wavelength, and eventually drop off for large arguments. Although the time ordered propagators retain negative values regions for arbitrary values of the weight $s$ for the measures, the restriction $2<s\leq d+1$ will guarantee the positivity for the amplitudes near the light cone.

hep-th↗

arXiv2023

Asymptotic entangled states from the dissipative interaction of two charged fields

We construct a field theory for dissipative systems using a hypercomplex ring formalism that reproduces naturally the effective doubling field formulation of dissipative systems of thermal field theory. The system is quantized by a noncanonical ansatz that gives the unitarity of the system is conserved. Asymptotically entangled states are constructed to introduce the study of the ergodicity of systems that undergo entanglement.

math-ph↗

arXiv2023

Strong/weak duality symmetries for Jacobi--Gordon field theory through elliptic functions

By using the scheme of Jacobi elliptic functions with their duality symmetries we present a formulation of the Jacobi- Gordon field theory that will manifest the strong/weak coupling duality at classical level; for certain continuous limits for the elliptic modulus the model will reduce to the standard sin/sinh Gordon field theories, for which such a strong/weak duality is known only at the level of the S-matrix. It is shown that the so called self-dual point for the standard sin/sinh Gordon field theory that divides the strong and the weak coupling regimes, corresponds only to one point of a set of fixed points under the duality transformations for the elliptic functions. The potentials constructed in terms of elliptic functions have a critical behavior near that self-dual point, showing a change of topology; in the weak coupling regime the vacuum topology implies that there exists the possibility of formation of topological defects, and in the strong regime coupling there no exists the possibility of formation of those defects. Furthermore, the equations of motion can be solved in exact form in terms of the inverse elliptic functions; in a case the kink-like solitons asso\-cia\-ted with the maxima of the potential can decay to cusp-like solitons associated with the minima. The polynomial expansions of the generalized models show a critical behavior at certain self-dual points; such points define the regions where the spontaneous symmetry breaking scenarios are po\-ssi\-ble. By invoking the duality symmetries for the elliptic functions, an explicit relation between the original potentials and their dual versions are constructed; with this relationship, an approaching to a specific self-dual point is considered for our generalized models.

hep-th↗

arXiv2022

Weighted Lorentz invariant measures as quantum field theory regulators

In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of the traditional formulations of quantum field theories, namely, smooth distributions for the field commutators that are finite a short distances, finite vacuum expectation values for the energy (without invoking normal ordering of operators), and finite fluctuations for the field operators. Our construction is based on a critical point of view on conventional quantum field theory statements, instead of invoking string theory inspired frameworks, since they are not necessary. We shall show that the conventional scheme for constructing quantum field theories has the necessary ingredients for obtaining generalized versions that, respecting the Lorentz symmetry, allows us to cure some of the divergences that plague the different formulations, particularly the ultra-violet divergences; additionally the present scheme will allows us to construct an infinite family of noncommutative field theories that are compared with other formulations. At the end, we discuss the impact of our formulation on particle physics numerology and on the cosmological constant problem

hep-th↗

arXiv2021

The Higgs mechanism and geometrical flows for two-manifolds

Using Perelman's approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum, and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the later scenario, the geometries at the degenerate vacua correspond to conformally flat manifolds without torsion; twisted two-dimensional geometries are obtained by building perturbation theory around a ground state; the tunneling quantum probability between vacua is determined along the flows.

hep-th↗

arXiv2020

Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography

The classical and quantum formulations for open systems related to dissipative dynamics are constructed on a complex hyperbolic ring, following universal symmetry principles, and considering the double thermal fields approach for modeling the system of interest, and the environment. The hyperbolic rotations are revealed as an underlying internal symmetry for the dissipative dynamics, and a chemical potential is identified as conjugate variable to the charge operator, and thus a grand partition function is constructed. As opposed to the standard scheme, there are not patologies associated with the existence of many unitarity inequivalent representations on the hyperbolic ring, since the whole of the dissipative quantum dynamics is realized by choosing only one representation of the field commutation relations. Entanglement entropy operators for the subsystem of interest and the environment, are constructed as a tool for study the entanglement generated from the dissipation. The holographic perspectives of our results are discussed.

hep-th↗

arXiv2020

Hyperbolic symmetries, inflaton-phantom cosmology, and inflation

Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is achieved along the universal prescriptions used in physics, avoiding the use of concepts as Euclideanization, non-canonical Lagrangians and hidden structures, that have appeared in other approaches. The scalar potentials constructed within the present scheme are bounded from below, and the realization of the spontaneous symmetry breaking of the aforementioned noncompact symmetry is studied. The profiles of these potentials with exact/broken hyperbolic symmetry replicate qualitative aspects of those ones used in inflationary models, and then a detailed com\-pa\-ri\-son is made. Moreover, the homotopy constraints of the topology induced on the corresponding vacuum manifolds, restricts the existence of topological defects associated with continuous symmetries, allowing only those defects associated with discrete symmetries; the consistency of these results is contrasted with current observational tests from the LIGO/Virgo collaboration, and terrestrial experiments based on a synchronized network of atomic magnetometers. At the end, the nonre\-la\-tivistic limit of the model is identified with a hyperbolic version of the nonlinear Schrödinger equation.

physics.gen-ph↗

arXiv2019

Constructing Lifshitz spaces using the Ricci flow

In this work we make use of the Ricci flow equations to show that, by starting from a general ansatz for the metric, we can construct two kinds of Lifshitz spaces in which: (a) the critical exponent coincides with the spatial dimension of the spacetime and therefore adopts discrete values, and (b) the critical exponent is continuous and arbitrary. These results show that Lifshitz spaces are exact solutions to the Ricci flow equations. Moreover, we found that the Ricci flow evolves towards a single fixed point for both cases which coincides with the flat spacetime.

hep-th↗

arXiv2019

A dynamical metric and its ground state from the breaking down of the topological invariance of the Euler characteristic

Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their continuous and discrete symmetries are discussed. The comparison with the so-called Chern-Simons state, which may be inappropriate as quantum state, allows us to conclude that the found wave functionals will give a plausible approximation to the ground state for the considered field theory.

hep-th↗

arXiv2018

Dynamical tachyonic AdS/QCD and information entropy

The configurational entropy setup is employed to study dynamical tachyonic holographic AdS/QCD models. The phenomenology of light-flavour mesonic states is then corroborated by the Shannon's information. Tachyonic bulk corrections to the dynamical AdS/QCD show more dominant and abundant dual mesonic states in the 4D boundary QCD, when compared to the dual mesons in the standard dynamical AdS/QCD. Entropic Regge-like trajectories are also emulated.

hep-th↗

arXiv2018

Evolution and metric signature change of maximally symmetric spaces under the Ricci flow

In this work we present solutions to the Ricci flow equations in arbitrary dimensions, particularizing for the $3d$ and $4d$ cases. We start by considering the $3d$ case and note that our solutions belong to the family of maximally symmetric spaces that can be extended to the $d\geq 4$ case following an analogue treatment. These solutions can be divided into two scenarios: maximally symmetric spaces with positive curvature i.e. de Sitter spaces, and maximally symmetric spaces with negative curvature i.e. Anti-de Sitter spaces. We show that between both scenarios there is a {\it critical point} where the curvature blows up along the flow. Also the solutions for $d\geq 4$ satisfy the flow equations with Riemannian or pseudo-Riemannian metrics due to the fact that the considered maximally symmetric spaces do not depend on time neither on the angular coordinates yielding equations that depend only on the radial coordinate and the Ricci flow parameter. Additionally we find an interesting effect of the flow consisting in a change of the signature of the metric when passing the singular point. Besides the signature change, the sign of the curvature also experiences a transition from positive to negative curvature, either with Riemannian or pseudo-Riemannian metrics throughout the singular point.

gr-qc↗

arXiv2017

Quantum field theory of a hyper-complex scalar field on a commutative ring

Inspired by the structural unification of unitary groups (quantum field theory) with orthogonal groups (relativity) proposed recently through a non-division algebra, we construct a hypercomplex field theory with an internal symmetry that unifies the U(1) compact gauge group with the SO(1,1) noncompact gauge group, using the commutative ring of hypercomplex numbers. From the quantum field theory point of view, the hypercomplex field encodes two charged bosons with opposite charge, and corresponds thus to a neutral compound boson. Furthermore, normal or- dering of operators is not required for controling the vacuum divergences; in an analogy with SUSY, the theory under study contains U(1) boson particles and their hyperbolic SO(1,1) boson partners, whose contributions to the vacuum energy cancel out exactly to a zero value. In fact the present scheme allows us to compare finite measuments of squeezed boson-number statistics obtained with and without normal ordering. Additionally we discuss on the potential applications of the squeezed boson states constructed on the commutative ring, in quantum teleportation and in related areas.

hep-th↗

arXiv2017

Symplectic analysis of three dimensional Abelian topological gravity

A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.

hep-th↗

arXiv2016

Hyperbolic deformation of a gauge field theory and the hierarchy problem

The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a U(1) field theory; in such a scheme a compact gauge group is deformed through a γ-parameter that varies along a non-compact internal direction, transverse to the U(1) compact one, and thus an additional SO(1,1) gauge symmetry is incorporated. This transverse direction can be understood as an extra internal dimension, which will control the spontaneous symmetry breakdown, and will allow us to establish a mass hierarchy. In this mechanism there is no brane separation to be stabilized as in the braneworld paradigm, however, a different kind of fine-tuning is needed in order to generate the wished electroweak/Planck hierarchy. By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in γ. Additionally the γ-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.

hep-th↗

arXiv2015

Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories

Inspired by the appearance of split-complex structures in the dimensional reduction of string theory, and in the theories emerging as byproducts, we study the hyper-complex formulation of Abelian gauge field theories, by incorporating a new complex unit to the usual complex one. The hypercomplex version of the traditional Mexican hat potential associated with the $U(1)$ gauge field theory, corresponds to a {\it hybrid} potential with two real components, and with $U(1)\times SO(1,1)$ as symmetry group. Each component corresponds to a deformation of the hat potential, with the appearance of a new degenerate vacuum. Hypercomplex electrodynamics will show novel properties, such as the spontaneous symmetry breaking scenarios with running masses for the vectorial and scalar Higgs fields, and the Aharonov-Bohm type strings defects as exact solutions; these topological defects may be detected only by quantum interference of charged particles through gauge invariant loop integrals. In a particular limit, the {\it hyperbolic} electrodynamics does not admit topological defects associated with continuous symmetries

hep-th↗