arXiv subjects

Harold Blas

Publications and source records attributed to Harold Blas.

At least 19 recordsLinked to original sources

arXiv2025

Hirota-tau and Heun-function framework for Dirac vacuum polarization and quantum stabilization of kinks

We investigate a modified affine Toda model coupled to matter (ATM) which includes a scalar self-interacting potential and demonstrate that its first-order integro-differential structure, preserving a deformed Noether-topological current correspondence, provides a consistent framework for fermion-soliton interactions. In this formulation, the fermion-soliton energy is proportional to the soliton's topological charge. We evaluate the renormalized energy functional, incorporating one-loop quantum corrections, and perform a variational minimization to determine the configuration that extremizes the functional. The fermionic back-reaction and the self-interacting scalar critically shape the fermion-kink energy, the in-gap bound-state spectrum, and the fermionic vacuum-polarization energy, yielding well-defined stability minima of the total energy as functions of the fermion and scalar masses and coupling parameters, in the semiclassical approximation. A key result is that the Heun-equation formalism is necessary to construct nonzero-energy bound and scattering states: unlike the tau-function method, which captures only the zero mode, the Heun approach encodes the full scattering data through local solution matching conditions. These results refine the spectral analysis of deformed integrable models. The stability of soliton-fermion configurations has direct implications for topologically protected states in quantum information and condensed-matter systems.

hep-th↗

arXiv2025

Riccati-type pseudo-potential approach to quasi-integrability of deformed soliton theories

This review paper explores the Riccati-type pseudo-potential formulation applied to the quasi-integrable sine-Gordon, KdV, and NLS models. The proposed framework provides a unified methodology for analyzing quasi-integrability properties across various integrable systems, including deformations of the sine-Gordon, Bullough-Dodd, Toda, KdV, pKdV, NLS and SUSY sine-Gordon models. Key findings include the emergence of infinite towers of anomalous conservation laws within the Riccati-type approach and the identification of exact non-local conservation laws in the linear formulations of deformed models. As modified integrable models play a crucial role in diverse fields of nonlinear physics-such as Bose-Einstein condensation, superconductivity, gravity models, optics and soliton turbulence-these results may have far-reaching applications.

hep-th↗

arXiv2024

Asymptotically conserved charges and 2-kink collision in quasi-integrable potential KdV models

We study a particular deformation of the potential KdV model (pKdV) and construct the quasi-conservation laws by a direct method. The charge densities, differing from their integrable counterpart with homogeneous degree terms, exhibit mixed scale dimension terms. The modifications of the charges around the soliton interaction regions are examined by numerically simulating some representative anomalies. We show numerically the elastic scattering of two kinks for a wide range of values of the deformation parameters. It is discussed an anomaly cancellation mechanism to define an exact conservation law of the usual pKdV model, and a renormalization procedure is introduced for some divergent charges by subtructing the continuous linear background contribution. The KdV-type equations are quite ubiquitous in several areas of non-linear science, such as the study of General Relativity in $AdS_{3}$, Bose-Einstein condensates, superconductivity and fluid dynamics.

hep-th↗

arXiv2024

Biorthogonal Majorana zero modes, ELC waves and soliton-fermion duality in non-Hermitian $sl(2)$ affine Toda coupled to fermions

We study a non-Hermitian (NH) $sl(2)$ affine Toda model coupled to fermions through soliton theory techniques and the realizations of the pseudo-chiral and pseudo-Hermitian symmetries. The interplay of non-Hermiticity, integrability, nonlinearity, and topology significantly influence the formation and behavior of a continuum of bound state modes (CBM) and extended waves in the localized continuum (ELC). The non-Hermitian soliton-fermion duality, the complex scalar field topological charges and winding numbers in the spectral topology are uncovered. The biorthogonal Majorana zero modes, dual to the NH Toda solitons with topological charges $\frac{2}π \arg{(z=\pm i)}=\pm 1$, appear at the complex-energy point gap and are pinned at zero energy. The zero eigenvalue $ł(z = \pm i)=0$, besides being a zero mode, plays the role of exceptional points (EPs), and each EP separates a real eigenvalue ${\cal A}$-symmetric and ${\cal A}$-symmetry broken regimes for an antilinear symmetry ${\cal A}\in \{ {\cal P}{\cal T}, \g_5{\cal P}{\cal T}\}$. Our findings improve the understanding of exotic quantum states, but also paves the way for future research in harnessing non-Hermitian phenomena for topological quantum computation, as well as the exploration of integrability and NH solitons in the theory of topological phases of matter.

hep-th↗

arXiv2017

Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges

We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities, split into two infinite towers of conserved and asymptotically conserved charges. For two-solitons without definite parity under space-reflection symmetry (kink-kink and kink-antikink scatterings with unequal and opposite velocities) our numerical results show the existence of the asymptotically conserved charges only. However, we show that in the center-of-mass reference frame of the two solitons the parity symmetries and their associated set of exactly conserved charges can be restored. Moreover, the positive parity breather-like (kink-antikink bound state) solution exhibits a tower of exactly conserved charges and a subset of charges which are periodic in time. We back up our results with extensive numerical simulations which also demonstrate the existence of long lived breather-like states in these models. The time evolution has been simulated by the 4th order Runge-Kutta method supplied with non-reflecting boundary conditions.

hep-th↗

arXiv2015

Space shifts of colliding ultrasonic dark solitons in deformed non-linear Schrödinger models

We derive a closed expression for the spatial shift experienced by a black soliton colliding with a shallow dark soliton in the context of deformed non-linear Schrödinger models. A perturbative scheme is developed based on the expansion parameter $1/(\g v)<<1$, where $v$ is the velocity of the incoming shallow dark soliton, $\g \equiv 1/\sqrt{1-v^2/v_s^2}$\, and $v_s$ is the Bogoliubov sound speed, therefore it is not restricted to small deformations of the integrable NLS model. As applications of our formalism we consider the integrable NLS model and the non-integrable cubic-quintic NLS model with non-vanishing boundary conditions. Extensive numerical simulations are performed in order to verify our results. A variant of the analysis for gray-gray soliton collision is discussed regarding a fast broad soliton and a slow thin soliton.

nlin.PS↗

arXiv2012

A fermion-soliton system: self-consistent solutions, vacuum polarization and charge quantization

An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions appear as an infinite number of topological sectors labeled by $n \in \IZ_{+}$, such that in each sector the scalar field would evolve continuously from a trivial configuration to the one with half integer topological charge. The spinor bound states are found analytically for each topological configuration of the background scalar field. The bound state energy satisfies an algebraic equation of degree $2n$, so the study of the energy spectrum finds a connection to the realm of algebraic geometry. We provide explicit computations for the topological sectors $n=1,2$. Then, by monitoring the energy spectrum, including the energy flow of any level across $E_n=0$, we discuss the vacuum polarization induced by the soliton. It is shown that the equivalence between the Noether and topological currents and the fact that the coupling constant is related to the one of the Wess-Zumino-Novikov-Witten (WZNW) model imply the quantization of the spinor and topological charges. Moreover, we show that the soliton mass as a function of the boson mass agrees with the Skyrmes's phenomenological conjecture. Our analytical developments improve and generalize the recent numerical results in the literature performed for a closely related model by Shahkarami and Gousheh, JHEP06(2011)116. The construction of the bound states corresponding to the topological sectors $n \geq 3$ is briefly outlined.

hep-th↗

arXiv2007

Generalized sine-Gordon model and baryons in two-dimensional QCD

We consider the sl(3,C) affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized sl(3,C) sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. The GSG models are multifield extensions of the ordinary sine-Gordon model. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents, which holds in the theory, it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement [JHEP0701(2007)027]. Moreover, the solitons and kinks of the generalized sine-Gordon (GSG) model are shown to describe the normal and exotic baryon spectrum of two-dimensional QCD. The GSG model arises in the low-energy effective action of bosonized QCD2 with unequal quark mass parameters [JHEP0703(2007)055]. The GSG potential for three flavors resembles the potential of the effective chiral lagrangian proposed by Witten to describe low-energy behavior of four dimensional QCD. Among the attractive features of the GSG model are the variety of soliton and kink type solutions for QCD2 unequal quark mass parameters. Exotic baryons in QCD2 [ Ellis and Frishman, JHEP0508(2005)081] are discussed in the context of the GSG model. Various semi-classical computations are performed improving previous results and clarifying the role of unequal quark masses. The remarkable double sine Gordon model also arises as a reduced GSG model bearing a kink(K) type solution describing a multi-baryon.

hep-th↗

arXiv2007

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

The solitons and kinks of the SU(3) generalized sine-Gordon model (GSG) are shown to describe the baryonic spectrum of two-dimensional quantum chromodynamics (QCD$_{2}$). The GSG model arises in the low-energy effective action of bosonized QCD$_{2}$ with unequal quark mass parameters. The GSG potential for $N_{f}=3$ flavors resembles the potential of the effective chiral lagrangian proposed by Witten to describe low-energy behavior of four dimensional QCD. Among the attractive features of the GSG model are the variety of soliton and kink type solutions for QCD$_{2}$ unequal quark mass parameters [JHEP(0701)(2007)(027)]. Exotic baryons in QCD$_{2}$ [J. Ellis et al JHEP0508(2005)081] are discussed in the context of the GSG model. Various semi-classical computations are performed improving the results of this reference and clarifying the role of unequal quark masses. The remarkable double sine Gordon model also arises as a reduced GSG model bearing a kink($K$) type solution describing a multi-baryon; so, the description of some resonances in QCD$_{2}$ may take advantage of the properties of the $K\bar{K}$ system.

hep-th↗

arXiv2005

Bosonized noncommutative bi-fundamental fermion and S-duality

We perform the path-integral bosonization of the recently proposed noncommutative massive Thirring model (NCMT$_{1}$) [JHEP0503(2005)037]. This model presents two types of current-current interaction terms related to the bi-fundamental representation of the group U(1). Firstly, we address the bosonization of a bi-fundamental free Dirac fermion defined on a noncommutative (NC) Euclidean plane $\IR_θ^{2}$. In this case we show that the fermion system is dual to two copies of the NC Wess-Zumino-Novikov-Witten model. Next, we apply the bosonization prescription to the NCMT$_{1}$ model living on $\IR_θ^{2}$ and show that this model is equivalent to two-copies of the WZNW model and a two-field potential defined for scalar fields corresponding to the global $U(1)\times U(1)$ symmetry plus additional bosonized terms for the four fermion interactions. The bosonic sector resembles to the one proposed by Lechtenfeld et al. [Nucl. Phys. B705(2005)477] as the noncommutative sine-Gordon for a {\sl pair} of scalar fields. The bosonic and fermionic couplings are related by a strong-weak duality. We show that the couplings of the both sectors for some representations satisfy similar relationships up to relevant re-scalings, thus the NC bi-fundamental couplings are two times the corresponding ones of the NC fundamental (anti-fundamental) and eight times the couplings of the ordinary massive Thirring and sine-Gordon models.

hep-th↗

arXiv2004

Bosonization and the generalized Mandelstam operators

The generalized massive Thirring model (GMT) with $N_{f}(=$number of positive roots of $su(n)$) fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with $N_{f}$ interacting soliton species. The generalized Mandelstam-Halpern soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. The examples of $su(3)$ and $su(4)$ are presented.

hep-th↗

arXiv2004

Bosonization and generalized Mandelstam soliton operators

The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(3) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag model like confinement mechanism and leading to the appearance of the massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank Lie algebra extension is also discussed.

hep-th↗

arXiv2004

Bosonization, soliton-particle duality and Mandelstam-Halpern operators

The generalized massive Thirring model (GMT) with $N_{f}$[=number of positive roots of $su(n)$] fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with $N_{f}$ interacting soliton species. The generalized Mandelstam-Halpern soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(n) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag model like confinement mechanism and leading to the appearance of the massive fermions (solitons). The $su(3)$ and $su(4)$ cases are discussed in detail.

hep-th↗

arXiv2004

Generalized sine-Gordon and massive Thirring models

We consider the Lagrangian description of the soliton sector of the so-called affine $\hat{sl}(3)$ Toda model coupled to matter (Dirac) fields (ATM). The theory is treated as a constrained system in the contexts of the Faddeev-Jackiw, the symplectic, as well as the master Lagrangian approaches. We exhibit the master Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The GMT model describes $N_{f}=3$ [number of positive roots of $su(3)$] massive Dirac fermion species with current-current interactions amongst all the U(1) species currents; on the other hand, the GSG theory corresponds to $N_{b}=2$ [rank of the $su(3)$ Lie algebra] independent Toda fields (bosons) with a potential given by the sum of three SG cosine terms. The dual description of the model is further emphasized by providing some on shell relationships between bilinears of the GMT spinors and the relevant expressions of the GSG fields. In this way, in the {\bf first part} of the chapter, we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model at the classical level. In the {\bf second part} of the chapter we give a full Lie algebraic formulation of the duality at the level of the equations of motion written in matrix form. The effective off-critical $\hat{sl}(3)$ ATM action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action plus some kinetic terms for the spinors and scalar-spinor interaction terms. Moreover, this theory still presents a remarkable equivalence between the Noether and topological currents, describes the soliton sector of the original model and turns out to be the master Lagrangian describing the GMT and GSG models.

hep-th↗

arXiv2003

Higher Grading Conformal Affine Toda Teory and (Generalized) Sine-Gordon/Massive Thirring Duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local Lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of $\hat{sl}(n) (n=2,3)$ is presented explicitly.

hep-th↗

arXiv2002

Affine Toda model coupled to matter and the string tension in QCD$_{2}$

The $sl(2)$ affine Toda model coupled to matter (ATM) is shown to describe various features, such as the spectrum and string tension, of the low-energy effective Lagrangian of QCD$_{2}$ (one flavor and $N$ colors). The corresponding string tension is computed when the dynamical quarks are in the {\sl fundamental} representation of SU(N) and in the {\sl adjoint} representation of SU(2).

hep-th↗

arXiv2002

Exact Foldy-Wouthuysen transformation for spin 0 particle in curved space

Up to now, the only known exact Foldy- Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one third of the relevant term in the fermionic case.

gr-qc↗

arXiv2001

Gravitational Rainbow

It is shown that unlike Einstein's gravity quadratic gravity produces dispersive photon propagation. The energy-dependent contribution to the deflection of photons passing by the Sun is computed and subsequently the angle at which the visible spectrum would be spread over is plotted as a function of the $R_{μν}^2-$sector mass.

gr-qc↗