Searcharxiv⌕ Search

arXiv subjects

Alfredo Raya

Publications and source records attributed to Alfredo Raya.

70 records · Page 4Linked to original sources
arXiv2011

Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics

We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.

hep-ph↗
arXiv2010

Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics and the 1/N approximation

We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient $θ$ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening --characteristic of the 1/N approximation-- is observed in the entire $(N,θ)$-plane through the local and global properties of the vector part of the fermion propagator.

hep-ph↗
arXiv2010

Free Form of the Foldy-Wouthuysen Transformation in External Electromagnetic Fields

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator $(γ\cdot Π)^2$, with $Π^μ= p^μ- e A^μ$. In this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.

math-ph↗
arXiv2010

Chiral and Parity Symmetry Breaking for Planar Fermions: Effects of a Heat Bath and Uniform External Magnetic Field

We study chiral symmetry breaking for relativistic fermions, described by a parity violating Lagrangian in 2+1-dimensions, in the presence of a heat bath and a uniform external magnetic field. Working within their four-component formalism allows for the inclusion of both parity-even and -odd mass terms. Therefore, we can define two types of fermion anti-fermion condensates. For a given value of the magnetic field, there exist two different critical temperatures which would render one of these condensates identically zero, while the other would survive. Our analysis is completely general: it requires no particular simplifying hierarchy among the energy scales involved, namely, bare masses, field strength and temperature. However, we do reproduce some earlier results, obtained or anticipated in literature, corresponding to special kinematical regimes for the parity conserving case. Relating the chiral condensate to the one-loop effective Lagrangian, we also obtain the magnetization and the pair production rate for different fermion species in a uniform electric field through the replacement $B\to-iE$.

hep-ph↗
arXiv2010

Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions

We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1)-dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one cartesian coordinate. Non-perturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and non-perturbative (homogeneous), are proportional to the external field, in agreement with early expectations.

hep-ph↗
arXiv2009

Impact of a uniform magnetic field and nonzero temperature on explicit chiral symmetry breaking in QED: Arbitrary hierarchy of energy scales

Employing the Schwinger's proper-time method, we calculate the $<\barψ ψ>$-condensate for massive Dirac fermions of charge $e$ interacting with a uniform magnetic field in a heat bath. We present general results for arbitrary hierarchy of the energy scales involved, namely, the fermion mass $m$, the magnetic field strength $\sqrt{eB}$ and temperature $T$. Moreover, we study particular regimes in detail and reproduce some of the results calculated or anticipated earlier in the literature. We also discuss possible applications of our findings.

hep-ph↗
arXiv2009

The Electron Propagator in External Electromagnetic Fields in Lower Dimensions

We study the electron propagator in quantum electrodynamics in lower dimensions. In the case of free electrons, it is well known that the propagator in momentum space takes the simple form $S_F(p)=1/(γ\cdot p-m)$. In the presence of external electromagnetic fields, electron asymptotic states are no longer plane-waves, and hence the propagator in the basis of momentum eigenstates has a more intricate form. Nevertheless, in the basis of the eigenfunctions of the operator $(γ\cdot Π)^2$, where $Π_μ$ is the canonical momentum operator, it acquires the free form $S_F(p)=1/(γ\cdot \bar{p}-m)$ where $\bar{p}_μ$ depends on the dynamical quantum numbers. We construct the electron propagator in the basis of the $(γ\cdot Π)^2$ eigenfunctions. In the (2+1)-dimensional case, we obtain it in an irreducible representation of the Clifford algebra incorporating to all orders the effects of a magnetic field of arbitrary spatial shape pointing perpendicularly to the plane of motion of the electrons. Such an exercise is of relevance in graphene in the massless limit. The specific examples considered include the uniform magnetic field and the exponentially damped static magnetic field. We further consider the electron propagator for the massive Schwinger model incorporating the effects of a constant electric field to all orders within this framework.

hep-th↗
arXiv2009

Chiral phase transition in relativistic heavy-ion collisions with weak magnetic fields: ring diagrams in the linear sigma model

Working in the linear sigma model with quarks, we compute the finite-temperature effective potential in the presence of a weak magnetic field, including the contribution of the pion ring diagrams and considering the sigma as a classical field. In the approximation where the pion self-energy is computed perturbatively, we show that there is a region of the parameter space where the effect of the ring diagrams is to preclude the phase transition from happening. Inclusion of the magnetic field has small effects that however become more important as the system evolves to the lowest temperatures allowed in the analysis.

hep-ph↗
arXiv2009

The Origin of Mass

Dynamical chiral symmetry breaking and confinement are two crucial features of Quantum Chromodynamics responsible for the nature of the hadron spectrum. These phenomena, presumably coincidental, can account for 98% of the mass of our visible universe. In this set of lectures, I shall present an introductory review of them in the light of the Schwinger-Dyson equations.

hep-ph↗
arXiv2008

Massive Dirac fermions and the zero field quantum Hall effect

Through an explicit calculation for a Lagrangian in quantum electrodynamics in (2+1)-space--time dimensions (QED$_3$), making use of the relativistic Kubo formula, we demonstrate that the filling factor accompanying the quantized electrical conductivity for massive Dirac fermions of a single species in two spatial dimensions is a half (in natural units) when time reversal and parity symmetries of the Lagrangian are explicitly broken by the fermion mass term. We then discuss the most general form of the QED$_3$ Lagrangian, both for irreducible and reducible representations of the Dirac matrices in the plane, with emphasis on the appearance of a Chern-Simons term. We also identify the value of the filling factor with a zero field quantum Hall effect (QHE).

hep-th↗
arXiv2008

Dynamical mass generation in QED with magnetic fields: arbitrary field strength and coupling constant

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetic fields of arbitrary strength, by solving the Schwinger-Dyson equation (SDE) for the fermion self-energy in the rainbow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass m for arbitrarily small values of electromagnetic coupling α. For intense fields it is also well known that m \propto \sqrt eB. Our approach allows us to span all regimes of parameters αand eB. We find that m \propto \sqrt eB provided αis small. However, when αincreases beyond the critical value α_c which marks the onslaught of dynamical fermion masses in vacuum, we find m \propto Λ, the cut-off required to regularize the ultraviolet divergences. Our method permits us to verify the results available in literature for the limiting cases of eB and α. We also point out the relevance of our work for possible physical applications.

hep-ph↗
arXiv2006

Dynamical mass generation in strongly coupled Quantum Electrodynamics with weak magnetic fields

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of weak magnetic fields using Schwinger-Dyson equations. Contrary to the case where the magnetic field is strong, in the weak field limit the coupling should exceed certain critical value in order for the generation of masses to take place, just as in the case where no magnetic field is present. The weak field limit is defined as eB << m(0)^2, where m(0) is the value of the dynamically generated mass in the absence of the field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB)^2.

hep-ph↗
arXiv2006

Finite size effects on pion spectra in relativistic heavy-ion collisions

We compute the pion inclusive transverse momentum distribution assuming thermal equilibrium together with transverse flow and accounting for finite size effects and energy loss at the time of decoupling. We compare to data on mid-rapidity pions produced in central collisions in RHIC at sqrt{s_{NN}}=200 GeV. We find that a finite size for the system of emitting particles results in a power-like fall-off of the spectra that follows the data up to larger p_t values, as compared to a simple thermal model.

hep-ph↗
arXiv2004

Comparison of alternative improved perturbative methods for nonlinear oscillations

We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt--Poincaré technique. As illustrative examples we choose one--dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.

math-ph↗
arXiv2004

Alternative perturbation approaches in classical mechanics

We discuss two alternative methods, based on the Lindstedt--Poincaré technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant.

math-ph↗