arXiv subjects

Carlos M. Reyes

Publications and source records attributed to Carlos M. Reyes.

At least 19 recordsLinked to original sources

arXiv2026

New constraints on modified gravity with dimension-six operators from gravitational waves

The present article deals with gravitational-wave propagation affected by higher-derivative terms that break spacetime symmetries. Two dimension-6 contributions of the gravitational Standard-Model Extension pose our starting point. A linearization of the action implies a wave equation that contains additional terms with spacetime-constant background fields. The modified dispersion relations in covariant form for gravitational waves are derived, where we distinguish between nonbirefringent and birefringent sectors. A classification of the coefficients in terms of sets with index structures resembling those of the electromagnetic fields has proven to be valuable. We constrain the nonbirefringent coefficients based on the measured arrival time difference between the gravitational wave and photons from the events GW170817 and GRB 170817A, respectively. Bounds on the birefringent coefficients result from the absence of a perceivable separation of the two modes in the event GW150914. These findings quantify the extent to which standard linearized gravity is valid based on the modifications considered.

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arXiv2026

Dipole ghosts and spontaneous symmetry breaking in higher-order Chern-Simons theory

In this work, we investigate the emergence of dipole ghost structures in gauge theories at both the classical and quantum levels. Traditionally, dipole ghosts are introduced through an auxiliary field $χ$ satisfying $\Box^2χ=0$, whose presence is reflected in the appearance of double poles in the propagator. We show that such dipole ghost sectors can instead be understood as a consequence of the multiplicity of solutions of the classical equations of motion. To establish this connection, we develop a constructive method and first apply it to covariant Maxwell theory in $(2+1)$ dimensions, where the essential ingredients can be identified in a transparent manner. We then extend the analysis to the constrained higher-order Chern-Simons theory, demonstrating that the same mechanism gives rise to dipole ghost sectors and associated double poles in the propagator. Our results provide a unified perspective on the origin of dipole ghosts, relating them directly to the degeneracy structure of the underlying classical dynamics. As a physical application, we investigate spontaneous symmetry breaking and compute the one-loop effective potential. We show that symmetry breaking removes the degeneracy underlying the dipole ghost sector, leading to a spectrum of ordinary massive gauge excitations that determine the quantum vacuum structure of the theory.

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arXiv2026

Gödel-symmetric backgrounds and explicit spacetime symmetry breaking

Explicit breaking of diffeomorphism symmetry with nondynamical background fields in gravitational theories can lead to inconsistencies between the equations of motion and the underlying pseudo-Riemannian geometry. These theories produce a constraint equation that follows from the modified Einstein's equations and the contracted Bianchi identity which has no simple solution and raises questions about the consistency of backgrounds structures in extensions to general relativity. In contrast, spontaneous symmetry breaking where fields acquire a vacuum expectation value are shown to avoid these problems. Nevertheless, there are some approaches that consistently implement explicit diffeomorphism breaking by: i) introducing geometrical restrictions which may dynamically restore diffeomorphism invariance, ii) using the Stückelberg formalism where auxiliary scalar fields can carry degrees of freedom associated to spontaneously broken symmetries, and more recently by iii) exploiting the isometries of a given gravitational configuration in the presence of a background; which ultimately requires the background fields to be Lie-dragged along the Killing vectors. In this work, we further develop and apply the latter approach focusing on a concrete example involving the Gödel metric and the minimal gravitational Standard-Model Extension. We show that the resulting dynamics is fully consistent with the constraint equation and produce new Noether's identities. Furthermore we investigate causality violations by analyzing the critical radius, which is found to depend explicitly on the background fields. This dependence allows for the emergence of both causal and non-causal regions in spacetime.

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arXiv2025

Higher-order Chern-Simons extensions to QED in $2+1$ dimensions

In this work, we investigate radiative corrections in the higher-order extension of the Maxwell-Chern-Simons model coupled to standard spinor matter in $2+1$ dimensions. We begin analyzing the higher-order gauge sector, where we find the modes and the polarizations vectors associated to a massive photon and ghost field. The higher-order gauge model is canonically quantized and as expected the resulting algebra of creation and annihilation operators corresponds to an indefinite metric in Hilbert space. Subsequently, we compute all relevant one-loop diagrams in the modified QED starting with the fermion self-energy. We show that the induced corrections to the fermion two-point function produce two independent fermionic degrees of freedom, which can be included in a redefined Lagrangian describing two decoupled fermions fields, one corresponding to a physical particle and the other to a negative-norm ghost state. We take advantage of this decomposition to compute the photon polarization operator and the vertex correction, both of which are found to be finite. Finally, we analyze the causal behavior of the model by computing the commutator of gauge fields at different spacetime points, and found that microcausality is preserved.

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arXiv2025

Reduced geometry and its role in explicit spacetime symmetry violation

The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an approach proposed originally by Stückelberg and the latter is to restrict spacetime geometry via the dynamical field equations and the second Bianchi identities. Moreover, a third technique is introduced in this work, which relies on isometries of a gravitational system. Our conclusion is that an SME background field configuration compatible with Riemannian geometry is more likely to be determined the more diffeomorphisms are isometries of the particular system. The proposal is demonstrated to work for cosmological time evolution with the SME backgrounds $u$ and $s^{μν}$ present. This finding has the potential to provide an alternative treatment of explicit spacetime symmetry violation in gravity.

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arXiv2024

Cosmology with explicit and spontaneous background fields

We study a general class of effective backgrounds that break diffeomorphism invariance and their potential roles in cosmology. Specifically, we examine both explicit and spontaneous background fields which display distinct transformation properties and are characterized with different dynamics. For explicit breaking, we focus on the $t$-sector of the minimal gravitational Standard-Model Extension (SME) and for spontaneous breaking on a vector field called the bumblebee model. In both cases, we derive the modified Friedmann equations and find a configuration of the background fields that preserve isotropy and homogeneity. We show that the explicit $t$-sector admits phases of accelerated expansion of the universe with standard matter.

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arXiv2024

Scalar sector of the Myers and Pospelov model: thermal and size effects

The scalar sector of the Myers and Pospelov model is considered. This theory introduces a dimension 5 operator with a preferred four-vector which breaks Lorentz symmetry. We investigate various applications using the TFD formalism, a topological field theory that allows the study of thermal and size effects on an equal footing. In this context, Lorentz-violating corrections to the Casimir effect and Stefan-Boltzmann law have been calculated.

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arXiv2023

The boundary of the gravitational Standard-Model Extension

A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a better understanding of the additional contributions that arise on the spacetime boundary $\partial M$. An extension of the previously introduced boundary terms, which are relevant in the context of asymptotically flat spacetimes, follows from the decomposition of $\partial M$ into timelike and spacelike hypersurfaces. Furthermore, we present an alternative method of deriving the field equations satisfied by the induced metric on the purely spacelike hypersurfaces of the foliated spacetime. This leads to the dynamical part of the Einstein equations modified by the background fields. Our results have the potential to be applicable in various contexts such as modified black holes and cosmology.

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arXiv2023

Perturbative S-matrix unitarity and higher-order Lorentz violation

We investigate the preservation of unitarity in a Lorentz and CPT-violating QED model containing higher-order operators. In particular, we consider modifications in the fermion sector with dimension-five operators. The higher-order operators lead to an indefinite metric and a pseudo-unitarity relation for the $S$-matrix. However, we show that the pseudo-unitarity condition can be promoted to a genuine unitarity relation by i) restricting the energies to the effective region far below the Planck mass and ii) considering stable particles to have positive metric. In the context of the optical theorem, we focus on the one-loop Bhabha and Compton scattering processes. We show that no ghost states get propagated through the cuts, thus satisfying the unitarity condition. Further, we show that discontinuities of propagators are equivalent to replacing physical Dirac functionals in the cutting equation. The physical Dirac functionals are defined to select only mode solutions of stable particles. The provided extension of Cutkosky rule may be helpful for analyzing perturbative unitarity in higher-order diagrams.

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arXiv2022

The ADM Formulation of the SME Gravity

The Hamiltonian formulation of the gravitational sector of the Standard-Model Extension (SME) with nondynamical fields $u$ and $s^{μν}$ is studied. We provide the relevant Hamiltonians that describe the constrained phase space and the dynamics of the induced metric on the ADM hypersurface. The generalization of the Gibbons-Hawking-York boundary term has been crucial to preventing second time-derivatives of the metric tensor in the Hamiltonians. By extracting the dynamics and constraints from the Einstein equations we have proved the equivalence between the Lagrangian and Hamiltonian formulations.

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arXiv2022

Tree-level unitarity, causality and higher-order Lorentz and CPT violation

Higher-order effects of CPT and Lorentz violation within the SME effective framework including Myers-Pospelov dimension-five operator terms are studied. The model is canonically quantized by giving special attention to the arising of indefinite-metric states or ghosts in an indefinite Fock space. As is well-known, without a perturbative treatment that avoids the propagation of ghost modes or any other approximation, one has to face the question of whether unitarity and microcausality are preserved. In this work, we study both possible issues. We found that microcausality is preserved due to the cancellation of residues occurring in pairs or conjugate pairs when they become complex. Also, by using the Lee-Wick prescription, we prove that the $S$ matrix can be defined as perturbatively unitary for tree-level $2\to 2$ processes with an internal fermion line.

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arXiv2022

Cosmology in the presence of diffeomorphism-violating, nondynamical background fields

We consider diffeomorphism violation, which is parameterized by nondynamical background fields of the gravitational Standard-Model Extension (SME), and study its effects on the time evolution of the Universe. Our goal is to identify background field configurations that imply stages of accelerated expansion without exotic forms of matter and radiation present. Although our approach gives rise to a set of restrictive conditions, configurations are encountered that exhibit this property or show other interesting behaviors. The findings of our article, which is among the first to apply the SME to a cosmological setting, provide an initial understanding of how to technically incorporate background fields into the cosmological evolution equations and what their phenomenological impact may be.

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arXiv2022

Modified-gravity theories with nondynamical background fields

We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{μν}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work. The computations show that the dynamical field equations obtained from the Lagrangian and Hamiltonian approaches are consistent with each other. Connections to Brans-Dicke theory and ghost-free massive gravity are established.

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arXiv2021

Hamiltonian formulation of an effective modified gravity with nondynamical background fields

The current paper is dedicated to developing a (3+1) decomposition for the minimal gravitational Standard-Model Extension. Our setting is explicit diffeomorphism violation and we focus on the background fields known in the literature as $u$ and $s^{μν}$. The Hamiltonian formalism is developed for these contributions, which amounts to deriving modified Hamiltonian and momentum constraints. We then study the connection between these modified constraints and the modified Einstein equations. Implications are drawn on the form of the background fields to guarantee the internal consistency of the corresponding modified-gravity theories. In the course of our analysis, we obtain a set of consistency requirements for $u$ and certain sectors of $s^{μν}$. We argue that the constraint structure remains untouched when these conditions are satisfied. Our results shed light on explicit violations of diffeomorphism invariance and local Lorentz invariance in gravity. They may turn out to be valuable for developing a better understanding of effective modified-gravity theories.

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arXiv2020

Optical theorem and indefinite metric in $λϕ^4$ delta-theory

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the $S$-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of $ξ^4$.

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arXiv2020

Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions

We canonically quantize $(2+1)$-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the Hamiltonian and the algebra satisfied by the field operators. The theory is characterized by an indefinite metric in the Hilbert space that brings up questions on causality and unitarity. We study both of the latter fundamental properties and show that microcausality as well as perturbative unitarity up to one-loop order are conserved when the Lee-Wick prescription is employed.

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arXiv2020

Unitarity in Maxwell-Carroll-Field-Jackiw electrodynamics

In this work we focus on the Carroll-Field-Jackiw (CFJ) modified electrodynamics in combination with a CPT-even Lorentz-violating contribution. We add a photon mass term to the Lagrange density and study the question whether this contribution can render the theory unitary. The analysis is based on the pole structure of the modified photon propagator as well as the validity of the optical theorem. We find, indeed, that the massive CFJ-type modification is unitary at tree-level. This result provides a further example for how a photon mass can mitigate malign behaviors.

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arXiv2018

Perturbative unitarity and higher-order Lorentz symmetry breaking

We study perturbative unitarity in the scalar sector of the Myers-Pospelov model. The model introduces a preferred four-vector $n$ which breaks Lorentz symmetry and couples to a five-dimension operator. When the preferred four-vector is chosen in the pure timelike or lightlike direction, the model becomes a higher time derivative theory, leading to a cubic dispersion relation. Two of the poles are shown to be perturbatively connected to the standard ones, while a third pole, which we call the Lee-Wick-like pole, is associated to a negative metric, in Hilbert space, threatening the preservation of unitarity. The pure spacelike case is a normal theory in the sense that it has only two solutions both being small perturbations over the standard ones. We analyze perturbative unitarity for purely spacelike and timelike cases using the optical theorem and considering a quartic self-interaction term. By computing discontinuities in the loop diagram, we arrive at a pinching condition which determines the propagation of particles and Lee-Wick-like particles through the cut. We find that the contribution for Lee-Wick-like particles vanishes for any external momenta, leaving only the contribution of particles, thus preserving one-loop unitarity in both cases.

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