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A. R. Aguirre

Publications and source records attributed to A. R. Aguirre.

At least 19 recordsLinked to original sources
arXiv2026

Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation

We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and Bäcklund-gauge formulations, we construct type-I and type-II defect matrices, derive the corresponding sewing conditions, and generate the bulk and defect contributions to an infinite hierarchy of conserved charges. The lowest members reduce to the standard sine-Gordon energy and momentum in the homogeneous limit, while for inhomogeneous backgrounds they define integrability-generated energy- and momentum-type quantities. Defect compatibility imposes matching conditions on the variable-mass functions across the defect. An analytical transmission factor $z$ characterizes soliton transmission, topological conversion, and absorption/emission processes. We then deform the type-I sewing conditions by parameters $α$ and $β$ and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for $αβ=1$, whereas for $αβ\neq 1$ parity-centered kink-kink and kink-antikink transmissions display vanishing lowest order integrated anomalies but no generic vanishing at higher order. Numerical simulations reproduce the integrable transmission/conversion regimes and show that non-integrable defects generate weak radiative tails and lowest order quasi-conserved charges, while quasi-conservation of the higher order charges remains unestablished. These results elucidate how exact defect integrability deforms into charge-dependent quasi-conservation and establish a framework for defect-controlled soliton transport in inhomogeneous media, with potential applications to nonuniform Josephson junctions, magnetic and nonlinear-optical systems, and effective molecular and DNA models.

hep-th↗
arXiv2025

New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies

A systematic construction for supersymmetric negative graded (non-local) flows for mKdV and KdV based on $sl(2,1)$ with a principal gradation is proposed in this paper. We show that smKdV and sKdV can be mapped onto each other through a gauge super Miura transformation, together with an additional condition for the negative flows, which ensure the supersymmetry of the negative sKdV flow. In addition, we classify both smKdV and sKdV flows with respect to the vacuum (boundary) solutions. These are classified according to zero or non-zero vacuum. Each vacuum solution is used to derive both soliton solutions and the corresponding Heisenberg subalgebra for the smKdV hierarchy. We present the new solutions corresponding to non-zero bosonic and fermionic vacuum by constructing the deformed vertex operators. Finally, the gauge Miura transformation is employed to obtain the sKdV solutions, which exhibit a rich degeneracy due to both multiple gauge super Miura transformations and multiple vacuum possibilities.

hep-th↗
arXiv2024

SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations

The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integrable hierarchies are then classified in terms of a decomposition of the underlying affine Lie algebra $\hat {\cal{G}} $ into graded subspaces defined by a grading operator $Q$. In this paper we shall discuss explicitly the simplest case of the affine $\hat {sl}(2)$ Kac-Moody algebra within the principal gradation given rise to the KdV and mKdV hierarchies and extend to supersymmetric models. It is known that the positive mKdV sub-hierachy is associated to some positive odd graded abelian subalgebra with elements denoted by $E^{(2n+1)}$. Each of these elements in turn, defines a time evolution equation according to time $t=t_{2n+1}$. An interesting observation is that for negative grades, the zero curvature representation allows both, even or odd sub-hierarchies. In both cases, the flows are non-local leading to integro-differential equations. Whilst positive and negative odd sub-hierarchies admit zero vacuum solutions, the negative even admits strictly non-zero vacuum solutions. Soliton solutions can be constructed by gauge transforming the zero curvature from the vacuum into a non trivial configuration (dressing method). Inspired by the dressing transformation method, we have constructed a gauge-Miura transformation mapping mKdV into KdV flows. Interesting new results concerns the negative grade sector of the mKdV hierarchy in which a double degeneracy of flows (odd and its consecutive even) of mKdV are mapped into a single odd KdV flow. These results are extended to supersymmetric hierarchies based upon the affine $\hat {sl}(2,1)$ super-algebra.

nlin.SI↗
arXiv2022

Spin-1/2 "bosons'' with mass dimension 3/2 and fermions with mass dimension 1 cannot represent physical particle states

We delve into the first principles of quantum field theory to prove that the so-called spin-1/2 ''bosons'' and the fermions with mass dimension 1, including ELKO, cannot represent physical particle states with spin $1/2$. Specifically, we first demonstrate that both aforementioned fields are not invariant under rotational symmetry, which implies that the particles created for these fields are not eigenstates of the spin operator in the $(\frac{1}{2},0)\oplus(0,\frac{1}{2})$ representation of the Lorentz group, nor is it possible to construct a Hamiltonian density scalar under the rotational group from them. Furthermore, following Weinberg's approach to local causal fields, we prove that regardless of any discrete symmetry or adjoint structure, the relativistic fields in the $(\frac{1}{2}, 0) \oplus (0,\frac{1}{2})$ representation satisfy the Fermi-Dirac statistics in complete agreement with the well-established spin-statistics theorem and experimental results.

hep-th↗
arXiv2021

Spin-half bosonic classification

In this paper, we define a new spinor classification that encompasses the recently proposed spin-half bosons with mass dimension three-half. As it will be shown, these particles, which are governed by a first-order equation and consequently provide a local theory, belong to a specific subclass of class-2 spinors within the bosonic classification, playing a similar role to Dirac spinors within the Lounesto classification. Such bosonic classification is shown to be closely connected with the usual fermionic Lounesto classification, and thus, evincing a symmetry between Dirac fermions and spin-half bosons.

hep-th↗
arXiv2021

The Lorentz-violating real scalar field at thermal equilibrium

In this paper we study Lorentz-Violation(LV) effects on the thermodynamics properties of a real scalar field theory due to the presence of a constant background tensor field. In particular, we analyse and compute explicitly the deviations of the internal energy, pressure, and entropy of the system at thermal equilibrium due to the LV contributions. For the free massless scalar field we obtain exact results, whereas for the massive case we perform approximated calculations. Finally, we consider the self interacting $ϕ^4$ theory, and perform perturbative expansions in the coupling constant for obtaining relevant thermodynamics quantities.

hep-th↗
arXiv2021

Spinorial structures, discrete symmetries and some consequences

In this paper we discuss fundamental aspects related to the helicity and dynamics of the spin-$1/2$ fermions encompassed within the very well-known Lounesto's classification. More specifically, we investigate how the bi-spinorial structures behave under discrete symmetries, as well as analyse some consequences on the spinors dynamics. In addition, we find an interesting relation between the spinor helicity and the Lounesto spinor classification.

math-ph↗
arXiv2020

Extended multi-scalar field theories in (1+1) dimensions

We present the explicit construction of some multi-scalar field theories in (1+1) dimensions supporting BPS (Bogomol'nyi--Prasad--Sommerfield) kink solutions. The construction is based on the ideas of the so-called extension method. In particular, several new interesting two-scalar and three-scalar field theories are explicitly constructed from non-trivial couplings between well-known one-scalar field theories. The BPS solutions of the original one-field systems will be also BPS solutions of the multi-scalar system by construction, and therefore we will analyse their linear stability properties for the constructed models.

hep-th↗
arXiv2020

Flag-dipole spinors: On the dual structure derivation and $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ symmetries

In this manuscript we report the flag-dipole spinors dual structure direct definition and analyze the properties behind the corresponding operator which generates such structure. This particular construction may be interesting for cosmological, phenomenological and mathematical physics applications. In addition, we analyse the behaviour of the flag-dipole spinors under action of discrete symmetries, facing an \emph{unconventional} property encoded on $(\mathcal{CPT})^2$.

math-ph↗
arXiv2019

A note on one-loop soliton quantum mass corrections

We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1+1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its corresponding tadpole graph contribution and use the renormalization prescription that such added term vanishes with adequate counterterms. As a result, we get a finite unambiguous formula for the soliton quantum mass corrections up to one-loop order, which turns to be independent of the chosen regularization scheme.

hep-th↗
arXiv2019

A hint towards mass dimension one Flag-dipole spinors

In this report we advance in exploring further details concerning the formal aspects of the construction of a Flag-dipole spinor. We report a (re-)definition of the dual structure which provide a Lorentz invariant and non-null norm, ensuring a local theory. With the new dual structure at hands, we look towards define relevant physical amounts, e.g., spin sums and quantum field operator. As we will see, the Flag-dipole and the Elko's theory are quite familar. In this vein, it is possible, via a matrix transformation, to write Flag-dipole spinors in terms of Elko spinor, evincing that both spinors are physically related and some physical amounts may be stated as equivalent.

hep-th↗
arXiv2019

Remarks on mass dimension one fermions: The underlying aspects, bilinear forms, Spinor Classification and RIM decomposition

In the present essay we review the underlying physical information behind the first concrete example describing a mass dimension one fermion - namely Elko spinors. We start the program exploring the physical information by evaluating the Elko bilinear forms, both within the proper orthochronous Lorentz subgroup as well as within the VSR theory. As we shall see, such structures do not hold the right observance of the Fierz-Pauli-Kofink quadratic relations. Thus, by the aforementioned reasons, we develop a deformation of the Clifford algebra basis. Such protocol can be accomplished by taking precisely the right Elko dual structure during the construction of the bilinear forms related to these spinors. With the appropriated bilinear forms at hands, we search for a real physical interpretation in order to achieve a deeper understanding of such spinor fields. Aiming an interesting application, we present a relation concerning Elko spinors and the neutrino physics via the Heisenberg non-linear theory by means of a bijective linear map between Elko spinors and the so-called Restricted Inomata-McKinley (RIM) spinors. Thus, we describe some of its properties. Some interesting results concerning the construction of RIM-decomposable spinors emerge from such prescription.

hep-th↗
arXiv2019

On the generalized spinor classification: Beyond the Lounesto's Classification

In this paper we advance into a generalized spinor classification, based on the so-called Lounesto's classification. The program developed here is based on an existing freedom on the spinorial dual structures definition, which, in a certain simple physical and mathematical limit, allows us to recover the usual Lounesto's classification. The protocol to be accomplished here gives full consideration in the understanding of the underlying mathematical structure, in order to satisfy the quadratic algebraic relations known as Fierz-Pauli-Kofink identities, and also to provide physical observables. As we will see, such identities impose a given restriction on the number of possible spinorial classes allowed in the classification. We also expose a mathematical device known as \emph{Clifford's algebra deformation}, which ensures real spinorial densities and holds the Fierz-Pauli-Kofink quadratic relations.

hep-th↗
arXiv2018

A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections

We consider one loop quantum corrections to soliton mass for the ${\cal N}=1$ supersymmetric extension of the (1+1)-dimensional scalar field theory with the potential $U(ϕ) = ϕ^2 \cos^2\left(\ln ϕ^2\right)$. First, we compute the one loop quantum soliton mass correction of the bosonic sector. To do that, we regularize implicitly such quantity by subtracting and adding its corresponding tadpole graph contribution, and use the renormalization prescription that the added term vanishes with the corresponding counterterms. As a result we get a finite unambiguous formula for the soliton quantum mass corrections up to one loop order. Afterwards, the computation for the supersymmetric case is extended straightforwardly and we obtain for the one loop quantum correction of the SUSY kink mass the expected value previously derived for the SUSY sine-Gordon and $ϕ^4$ models. However, we also have found that for a particular value of the parameters, contrary to what was expected, the introduction of supersymmetry in this model worsens ultraviolet divergences rather than improving them.

hep-th↗
arXiv2018

Recursion Operator and Bäcklund Transformation for Super mKdV Hierarchy

In this paper we consider the ${\cal N}=1$ supersymmetric mKdV hierarchy composed of positive odd flows embedded within an affine $\hat sl(2,1)$ algebra. Its Bäcklund transformations are constructed in terms of a gauge transformation preserving the zero curvature representation. The recursion operator relating consecutive flows is derived and shown to relate their Bäcklund transformations.

nlin.SI↗
arXiv2018

Defects in the supersymmetric mKdV hierarchy via Backlund transformations

The integrability of the ${\cal N}=1$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation is performed by using essentially two methods: the Bäcklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the Bäcklund equations in components for the first few flows of the hierarchy, namely $t_3$ and $t_5$. Secondly, the supersymmetric extension of the Bäcklund transformation in the superspace formalism is constructed for those flows. Finally, this super Bäcklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.

math-ph↗
arXiv2016

The sinh-Gordon defect matrix generalized for n defects

In this paper we obtain a general expression for the n-defect matrix for the sinh-Gordon model. This in turn generate the general Bäcklund transformations (BT) for a system with $n$ type-I defects, through a gauge transformation.

nlin.SI↗