Related papers: Polyakov's spin factor and new algorithms for effi…
The proper time path integral representation is derived explicitly for an arbitrary $n$-point amplitude in QCD. In the standard perturbation theory the formalism allows to sum up the leading subseries, e.g. yielding double-logarithm Sudakov…
For the `classical' formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization…
The worldline casting of a gauge field system with spin-1/2 matter fields has provided a, particle-based, first quantization formalism in the framework of which the Bern-Kosower algorithms for efficient computations in QCD acquire a simple…
The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one…
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…
The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
The applicability of the space-time formulation of the gluonic sector of QCD in terms of the Polyakov worldline path integral, via the use of the background field gauge fixing method, is extended to multi-gluon loop configurations. Relevant…
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative…
The Wilson contour integral approach is applied to resum the soft gluon radiative correctins to the quark form factors in the Sudakov regime. The one-loop order results for the quark-photon (color singlet form factor) and quark-gluon (color…
An approach to approximate evaluation of the continuum Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
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…
Sudakov form factors appear ubiquitously in factorized cross sections where they allow one to resum large logarithms to all orders in perturbation theory. Their exact evaluation requires numerical integrals over anomalous dimensions, which…
A simple derivation of the free energy and expectation values of Polyakov-loops in $QCD_2$ via path integral methods is given. In the chosen gauge (which can be generalized to 4 dimensions) without Gribov-copies the Fadeev-Popov determinant…
The asymptotics of n-point Green's function at large external momenta is obtained in the exponentiated form using the Fock-Feynman-Schwinger representation for propagators in the external field. The method is applied to gauge theories such…