Related papers: New Approach to Continuum Path Integrals for Parti…
Time derivatives of scalar fields occur quadratically in textbook actions. A simple Legendre transformation turns the lagrangian into a hamiltonian that is quadratic in the momenta. The path integral over the momenta is gaussian. Mean…
This paper reviews and generalizes Feynman's path integration methods which use time slicing with straight line segments and Fourier sine series. The generalizations are done from variational calculus considerations and in one dimension for…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge…
In the Feynman-Kac[1] path integral approach the eigenvalues of a quantum system can be computed using Wiener measure which uses Brownian particle motion. In our previous work[2-3] on such systems we have observed that the Wiener process…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical…
Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…
After the first detection of a gravitational wave in 2015, the number of successes achieved by this innovative way of looking through the universe has not stopped growing. However, the current techniques for analyzing this type of events…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
Considering (euclidean) quantum gravity in the Einstein-Hilbert truncation, we calculate the one-loop effective action $\Gamma^{1l}_{\rm grav}$ using a spherical background. Usually, this calculation is performed resorting to proper-time…
We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…
The reality and convexity of the effective potential in quantum field theories has been studied extensively in the context of Euclidean space-time. It has been shown that canonical and path-integral approaches may yield different results,…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we…
The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on two distinct frameworks: field theories…
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…
We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and…