Related papers: Path integrals and stochastic calculus
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
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…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
We develop a general framework for pathwise stochastic integration that extends F\"ollmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of It\^o, Stratonovich,…
Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time…
We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path indexed by a square, satisfying some H\"older regularity…
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…
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…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…