相关论文: Path Integration on Darboux Spaces

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…

A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main…

We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces - an algebraic invariant…

The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…

We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…

A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…

The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to give for the first time a negative answer to an old question of quantum mechanics in curved spaces raised in 1957 by…

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…

We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…

A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…

We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is…

For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…

Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…

The Feynman path integral is defined over the space $\mathbb{R}^T$ of all possible paths; it has been a powerful tool to develop Quantum Mechanics. The absolute value of Feynman's integrand is not integrable, then Lebesgue integration…

Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…

The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) \otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of…

The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…

We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…