Related papers: Stochastic mechanics and the Feynman integral
We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
We construct quantum stochastic integrals for the integrator being a martingale in a von Neumann algebra, and the integrand -- a suitable process with values in the same algebra, as densely defined operators affiliated with the algebra. In…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…
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,…
In this work, the role of a time-varying Newton constant under the scale-dependent approach is investigated in the thermodynamics of the Friedman equations. In particular, we show that the extended Friedman equations can be derived either…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
The subject of this work is to apply the modified Feynman disentangling approach to a problem of transitions in a non-quadratic quantum-mechanical system: a singular oscillator with a time-dependent frequency.
We provide evidence that quantum mechanics can be interpreted as a rational algorithm for finding the least complex description for the correlations in the outputs of sensors in a large array. In particular, by comparing the…
We give two novel proofs that the path integral and stochastic quantizations of generic scalar Euclidean quantum field theories are equivalent. Our proofs rely on Taylor interpolations indexed by forests, in the fashion of constructive…
In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function.…
We discuss how the stochastic approach for supersymmetric theories leads to new ways of characterizing anomalies in how supersymmetry can be broken.
We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…
In this paper I will review some basic aspects of the mechanism of stochastic resonance. Stochastic resonance was first introduced as a possible mechanism to explain long term climatic variation. Since then, there have been many…
Stochastic semiclassical gravity of the 90's is a theory naturally evolved from semiclassical gravity of the 70's and 80's. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy…
We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to exp(-E/kT) where E is…
We consider the stochastic transport equation where the randomness is given by the symmetric integral with respect to stochastic measure. For stochastic measure, we assume only $\sigma$-additivity in probability and continuity of paths. The…