Related papers: Worldline path integral for the massive Dirac prop…
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…
The resolvent of supersymmetric Dirac Hamiltonian is studied in detail. Due to supersymmetry the squared Dirac Hamiltonian becomes block-diagonal whose elements are in essence non-relativistic Schr\"odinger-type Hamiltonians. This enables…
We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of…
We study the spin factor problem both in $3+1$ and $2+1$ dimensions which are essentially different for spin factor construction. Doing all Grassmann integrations in the corresponding path integral representations for Dirac propagator we…
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…
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…
Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over non-relativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
We study the Dirac propagator dressed by an arbitrary number $N$ of photons by means of a worldline approach, which makes use of a supersymmetric ${\cal N} = 1$ spinning particle model on the line, coupled to an external Abelian vector…
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length,…
We consider the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates and derive a functional analytic integral representation of the associated propagator using the…
We construct a worldline path integral for the effective action and propagator of a Dirac field in 2+1 dimensions in an Abelian gauge field background. Integrating over an auxiliary gauge group variable we derive a worldline action…
We study the realization of chiral and parity transformations within a particle-like path-integral representation for Dirac fields, showing how those transformations can be implemented in a natural way within the formalism. We then obtain a…
The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is…
The relativistic Green's function of a free spin-1/2 fermion is derived using the Feynman path integral formalism in spherical coordinates. The Green's function is reduced to an exactly solvable path integral by an appropriate coordinate…
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…
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…
The proper time formalism for a particle propagator in an external electromagnetic field is combined with the path-dependent formulation of the gauge theory to simplify the quasiclassical propagator. The latter is achieved due to a specific…
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…