arXiv subjects

Mauricio Valenzuela

Publications and source records attributed to Mauricio Valenzuela.

At least 19 recordsLinked to original sources

arXiv2026

Carrollian Wave Equations for Arbitrary Spin: Anyons and the Exotic Particle on the Noncommutative Plane

We construct the Carrollian limit of the Cort\'es--Plyushchay wave equations for planar anyons, grading the spin-tower components by powers of $c$ and taking the limit at fixed rest energy. The result is a linear system describing Carrollian particles of any real spin --- \emph{Carrollian anyons} --- and, at (half-)integer spin, Carrollian bosons, fermions and higher-spin fields. The system is a first-order square root of the standard Carroll wave equation $(\partial_t^2+E^2)\Phi=0$, whose spectrum consists of two flat branches at plus and minus the rest energy. Scaling the spin along with $c$, in the Carrollian analogue of the Jackiw--Nair limit, yields instead the exotic Carroll algebra, with a second central charge, non-commuting boosts, and observable coordinates spanning a noncommutative plane. We show how the Galilean and Carrollian theories branch from one common similarity transformation: the Galilean limit expels the negative-energy modes, whereas the Carroll limit retains both relativistic branches.

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arXiv2026

Interacting Galilean and Finite-Energy Carroll Fermions

We present a unified derivation of the Galilean and Carrollian limits of the massive Dirac action based on a similarity transformation depending on the mass and the speed of light. The two choices of Dirac conjugation, combined with different mass scalings, generate distinct families of limiting actions. This construction recovers known Galilei and Carroll fermion models and yields new systems, one in each regime. We classify a sufficient set of boost-compatible local (self-)interactions, which includes Nambu--Jona-Lasinio (NJL). The new Galilean free action possesses a local fermionic gauge symmetry that eliminates its local field content. A selected quartic interaction, preserving the Bargmann boost, explicitly breaks the original fermionic gauge symmetry so that the argument that eliminates the field content no longer applies. The NJL limit interaction merely deforms the realization of that gauge symmetry. We show that the energy parameter in several Carroll actions can be eliminated by a time-dependent phase redefinition; conversely, in the new Carrollian extension the energy cannot be removed.

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arXiv2024

Massless Rarita-Schwinger equations: Half and three halves spin solution

Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -- free of arbitrary functions of time -- we argue that the often-invoked residual gauge symmetry lacks fundamental grounding and should not be used to enforce new external constraints. The result is verified by the total Hamiltonian dynamics. We conclude that eliminating the spin-12 mode \textit{via} the extended Hamiltonian dynamics would be acceptable if the Dirac conjecture was assumed; however, this framework does not accurately describe the original Lagrangian system.

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arXiv2023

Gauge and time-reparametrization invariant spin-half fields

We present a fermion model characterized by an anticommuting-parameter shift symmetry. The Hamiltonian formulation exhibits a combination of first-class and second-class constraints. We derive the well-known Dirac equation by fixing the gauge in a covariant manner, enabling the fields to propagate accordingly. Notably, the model inherently possesses invariance under reparametrizations of time. Consequently, the Hamiltonian vanishes, setting it apart from the conventional framework of Dirac's theory. Furthermore, we establish a correspondence between these particles and the zero-modes of the massless Rarita-Schwinger system, bringing forth the intriguing implication that they may describe a supergravity ground state.

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arXiv2023

Quantization of counterexamples to Dirac's conjecture

Dirac's conjecture, that secondary first-class constraints generate transformations that do not change the physical system's state, has various counterexamples. Since no matching gauge conditions can be imposed, the Dirac bracket cannot be defined, and restricting the phase space first and then quantizing is an inconsistent procedure. The latter observation has discouraged the study of systems of this kind more profoundly, while Dirac's conjecture is assumed generally valid. We point out, however, that secondary first-class constraints are just initial conditions that do not imply Poisson's bracket modification, and we carry out the quantization successfully by imposing these constraints on the initial state of the wave function. We apply the method to two Dirac's conjecture counterexamples, including Cawley's iconical system.

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arXiv2023

Pseudoclassical system with gauge and time-reparametrization invariance

We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the Dirac conjecture does not hold -- the secondary first-class constraint is not a symmetry generator -- and only the gauge fixing condition associated with the primary first-class constraint is needed to remove the gauge ambiguities. The gauge fixed theory is equivalent to the Fermi harmonic oscillator extended by a boundary term. We quantize in the deformation quantization and in the Schrodinger representation approaches and observe that the boundary term prepares the system in the state of positive energy.

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arXiv2023

Electromagnetically and gravitationally stealth fields

We construct a generic class of models for complex scalar fields -- minimally coupled to gravity and electromagnetism -- with the property that their energy-momentum tensor and the electric current vanish for certain massive configurations. These are electromagnetically and gravitationally {\it stealth fields}. We shall see that the latter configurations can affect, in addition, the strength of the gravity-matter and electromagnetic-matter couplings of other (non-stealth) modes present in the system, which turn out to be equivalent to the re-scaling the electric charge and the Newton constant (with a stealth-mass depending factor).

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arXiv2023

On the spin content of the classical massless Rarita--Schwinger system

We analyze the Rarita--Schwinger (RS) massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a spin-1/2 and a spin-3/2 propagating Poincaré group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture--that all first class constraints generate gauge symmetries--is assumed or not. In the affirmative case, a secondary first class constraint must be added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the spin-1/2 sector. In the opposite case, the spin-1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.

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arXiv2021

$\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity

We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator in the form of an outer automorphism of $su(2,2|2)$-valued 2-form tensors. The model closely resembles a Yang-Mills theory -- including the action principle, equations of motion and gauge transformations -- which avoids the use of the otherwise complicated component formalism. The theory enjoys $H=SO(3,1)\times \mathbb{R} \times U(1)\times SU(2)$ off-shell symmetry whilst the broken symmetries $G/H$, translation-type symmetries and supersymmetry, can be recovered on surface of integrability conditions of the equations of motion, for which it suffices the Rarita-Schwinger equation and torsion-like constraints to hold. Using the \textit{matter ansatz} -- projecting the $1 \otimes 1/2$ reducible representation into the spin-$1/2$ irreducible sector -- we obtain (chiral) fermion models with gauge and gravity interactions.

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arXiv2021

A pedagogical discussion of N = 1 four-dimensional supergravity in superspace

A short introduction to N = 1 supergravity in four dimensions in the superspace approach is given emphasising on all steps to obtain the final Lagrangian. In particular starting from geometrical principles and the introduction of superfields in curved superspace, the action coupling matter and gauge fields to supergravity is derived. This review is based on the book -A supergravity Primer: From geometrical principles to the Final Lagrangian- and on several lectures given at the doctoral school of Strasbourg.

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arXiv2021

Unconventional SUSY and Conventional Physics: A Pedagogical Review

In supersymmetric extensions of the Standard Model, the observed particles come in fermion-boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a single supersymmetric pair has been reported to date. Although a hypothetical SUSY breaking mechanism, operating at high energy inaccessible to current experiments cannot be ruled out, this reduces SUSY's predictive power and it is unclear whether SUSY, in its standard form, can help reducing the remaining puzzles of the standard model (SM). Here we argue that SUSY can be realized in a different way, connecting spacetime and internal bosonic symmetries, combining bosonic gauge fields and fermionic matter particles in a single gauge field, a Lie superalgebra-valued connection. In this unconventional representation, states do not come in SUSY pairs, avoiding the doubling of particles and fields and SUSY is not a fully off-shell invariance of the action. The resulting systems are remarkably simple, closely resembling a standard quantum field theory and SUSY still emerges as a contingent symmetry that depends on the features of the vacuum/ground state. We illustrate the general construction with two examples: i) A 2+1 dimensional system based on the $osp(2,2|2)$ superalgebra, including Lorentz and $u(1)$ generators that describes graphene; ii) A supersymmetric extension of 3+1 conformal gravity with an $SU(2,2|2)$ connection that describes a gauge theory with an emergent chiral symmetry breaking, coupled to gravity. The extensions to higher odd and even dimensions, as well as the extensions to accommodate more general internal symmetries are also outlined.

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arXiv2020

Chiral gauge theory and gravity from unconventional supersymmetry

From a gauge $SU(2,2|2)$ model with broken supersymmetry, we construct an action for $SU(2)\times U(1)$ Yang-Mills theory coupled to gravity and matter. The connection components for AdS boosts and special conformal translations are auxiliary fields and their fixing reduces the theory to two distintive sectors: a vector-like gauge theory with general relativity and a chiral gauge theory where gravity drops out. We discuss some of the main classical features of the model such as the predicted tree level gauge couplings, cosmological constant value, mass-like terms and the Einstein equations.

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arXiv2018

Higher Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics

The dynamical symmetries of $1+1$-dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial De Alfaro-Fubini-Furlan, DFF, damping term) are investigated. The first-order invariant differential operators induce several invariant algebras and superalgebras. Besides the $sl(2)\oplus u(1)$ invariance of the Calogero Conformal Mechanics, an $osp(2|2)$ invariant superalgebra, realized by first-order and second-order differential operators, is obtained. The invariant algebras with an infinite tower of generators are given by the universal enveloping algebra of the deformed Heisenberg algebra, which is shown to be equivalent to a deformed version of the Schrödinger algebra. This vector space also gives rise to a higher spin (gravity) superalgebra. We furthermore prove that the pure and DFF Matrix Calogero PDEs possess isomorphic dynamical symmetries, being related by a similarity transformation and a redefinition of the time variable.

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arXiv2018

Massive stealth scalar fields from field redefinition method

We propose an uni-parametric deformation method of action principles of scalar fields coupled to gravity which generates new models with massive stealth field configurations, i.e. with vanishing energy-momentum tensor. The method applies to a wide class of models and we provide three examples. In particular we observe that in the case of the standard massive scalar action principle, the respective deformed action contains the stealth configurations and it preserves the massive ones of the undeformed model. We also observe that, in this latter example, the effect of the energy-momentum tensor of the massive (non-stealth) field can be amplified or damped by the deformation parameter, alternatively the mass of the stealth field.

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arXiv2018

From phase space to multivector matrix models

Combining elements of twistor-space, phase space and Clifford algebras, we propose a framework for the construction and quantization of certain (quadric) varieties described by Lorentz-covariant multivector coordiantes. The correspondent multivectors can be parametrized by second order polynomials in the phase space. Thus the multivectors play a double role, as covariant objects in $D=2,3,4 \texttt{ Mod } 8$ space-time dimensions, and as mechanical observables of a non-relativistic system in $2^{[D/2]-1}$ euclidean dimensions. The latter attribute permits a dual interpretation of concepts of non-relativistic mechanics as applying to relativistic space-time geometry. Introducing the Groenewold-Moyal *-product and Wigner distributions in phase space induces Lorentz-covariant non-commutativity and it provides the spectra of geometrical observables. We propose also new (multivector) matrix models, interpreted as descending from the interaction term of a Yang-Mills theory with minimally coupled massive fermions, in the large-$N$ limit, which serves as a physical model containing the constructed multivector (fuzzy) geometries. We also include a section on speculative aspects on a possible cosmological effect and the origin of space-time entropy.

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arXiv2017

Higher spin matrix models

We propose a hybrid class of theories for higher spin gravity and matrix models, i.e. which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev's higher spin gravity but part of the equations of motion are provided by the action principle of a matrix model. In particular we construct a higher spin (gravity) matrix model related to type IIB matrix models/string theory which have a well defined classical limit, and which is compatible with higher spin gravity in $AdS$ space. As it has been suggested that higher spin gravity should be related to string theory in a high energy (tensionless) regime, and therefore to M-Theory, we expect that our construction will be useful to explore concrete connections.

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arXiv2016

3D Higher spin gravity and the fractional quantum Hall effect

This article is based on the talk "Fractional Spin Gravity" presented in the 31st International Colloquium on Group Theoretical Methods in Physics, Rio de Janeiro, 19-25th June 2016. There we emphasised an implication of the works [1,2] by N. Boulanger, P. Sundell and the author on fractional spin extensions of 2+1D higher spin gravity. This is that higher spin gravity may govern interactions of pseudo-particles excitations in the (fractional) quantum Hall effect. More generally, fractional spin currents in 2+1D source higher spin gravity curvatures.

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arXiv2016

Higher-spin symmetries of the free Schrodinger equation

It is shown that the Schrodinger symmetry algebra of a free particle in d spatial dimensions can be embedded into a representation of the higher-spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrodinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of non-relativistic generators. We show also how to convert Vasiliev's equations into an explicit non-relativistic covariant form, such that they might apply to non-relativistic systems. Our procedure reveals that the space of solutions of the Schrodinger equation can be regarded also as a supersymmetric module.

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