相关论文: Path Integral in Holomorphic Representation withou…

The strictly gauge invariant approach to the construction of the analog of guiding center integrals of motion in spatially homogeneous/inhomogeneous constant magnetic fields is considered. With their help the gauge invariant equations,…

In this paper we study the quantum evolution in a flat Riemannian manifold. The holomorphic functions are defined on the cotangent bundle of this manifold. We construct Hilbert spaces of holomorphic functions in which the scalar product is…

Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's…

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…

We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…

Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in…

Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…

This paper provides a pedagogical introduction to the quantum mechanical path integral and its use in proving index theorems in geometry, specifically the Gauss-Bonnet-Chern theorem and Lefschetz fixed point theorem. It also touches on some…

We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the $T$-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious…

Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation.…

A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…

Using the notion of distribution on an infinite dimensional space defined in our previous paper, we give definition of a version of dynamical evolution in quantum field theory, motivated by heuristic formulas involving path integrals.

A set of differential operators acting by continuous deformations on path dependent functionals of open and closed curves is introduced. Geometrically, these path operators are interpreted as infinitesimal generators of curves in the base…

The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…

We briefly review a hamiltonian path integral formalism developed earlier by one of us. An important feature of this formalism is that the path integral quantization in arbitrary co-ordinates is set up making use of only classical…

We consider methods for constructing explicit solutions of the non-stationary Lam\'e equation, which is a generalization of the classical Lam\'e equation, that has appeared in works on integrable models, conformal field theory, high energy…

We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in…

Off-shell supersymmetry, which restricts sparticles to appear only off-shell, solves the gauge hierarchy problem and unifies the gauge couplings in the usual way. Without introducing any new interactions or exacerbating the naturalness,…