Related papers: Chirality and parity in a first-quantized represen…
We derive some non-perturbative results in 1+1 and 2+1 dimensions within the context of the particle path-integral representation for a Dirac field propagator in the presence of an external field, in a formulation introduced by Migdal in…
We present different non-perturbative calculations within the context of Migdal's representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar…
It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$…
We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
The paper offers an expression of the general Foldy-Wouthuysen transformation in the chiral representation of Dirac matrices and in the presence of boson fields interacting with fermion field.
We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition,…
For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality…
Explicit exact formulas are presented, for the leading order term in a strict chiral covariant derivative expansion, for the abnormal parity component of the effective action of two- and four-dimensional Dirac fermions in presence of…
We proceed with the construction of normalizable Dirac wave packets for treating chiral oscillations in the presence of an external magnetic field. Both chirality and helicity quantum numbers correspond to variables of fundamental…
We propose a nonperturbative formulation of chiral gauge theories. The method involves a `pre-regulation' of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of…
Reporting about the formalism with the Dirac equation we describe the dynamics of chiral oscillations for a fermionic particle non-minimally coupling with an external magnetic field. For massive particles, the chirality and helicity quantum…
Explicit exact formulas are presented, up to fourth order in a strict chiral covariant derivative expansion, for the normal parity component of the Euclidean effective action of even-dimensional Dirac fermions. The bosonic background fields…
The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix, these equations possess…
The overlap formula for the chiral determinant is presented and the realization of gauge anomalies and gauge field toplogy in this context is discussed. The ability of the overlap formalism to deal with supersymmetric theories and…
The chiral Dirac determinant is calculated using the overlap formalism of Narayanan and Neuberger. We compare the real and imaginary parts of the determinant with the continuum result for perturbative gauge field backgrounds and show that…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
A variant for the superspin one-half massive superparticle in $ 4D $, $ \mathcal{N}=1 $, based on Dirac superfields, is offered. As opposed to the current known models that use spinor chiral superfields, the propagating fields of the…
A representation for the phase of a chiral determinant in terms of a path integral of a local action is constructed. This representation is used to modify the action of chiral SU(2) fermions removing the global anomaly.
We review the parity anomaly of the massless Dirac fermion in $2+1$ dimensions from the Hamiltonian, as opposed to the path integral, point of view. We have two main goals for this note. First, we hope to make the parity anomaly more…