Related papers: Path integrals for awkward actions

The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…

Path integral Monte Carlo (PIMC) simulations have become an important tool for the investigation of the statistical mechanics of quantum systems. I discuss some of the history of applying the Monte Carlo method to non-relativistic quantum…

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for…

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral…

An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…

The behavior of the one-dimensional random-force-driven Burgers equation is investigated in the path integral formalism on a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…

Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the…

This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a radial basis function expansion of the interaction term that appears in…

Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. In the context of an annealed sequence of distributions, field transformations are defined by integrating…

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at…

Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as…

I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to…

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…

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…

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…

Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…

We derive an effective classical theory for real-time SU($N$) gauge theories at high temperature. By separating off and integrating out quantum fluctuations we obtain a 3D classical path integral over the initial fields and conjugate…

On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…