Related papers: Path Integrals in Quantum Physics
A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
We propose path integral description for quantum mechanical systems on compact graphs consisting of N segments of the same length. Provided the bulk Hamiltonian is segment-independent, scale-invariant boundary conditions given by…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
In this article we will explore the concept of speedrunning as a representation of a simplified version of quantum mechanics within a classical simulation. This analogy can be seen as a simplified approach to understanding the broader idea…
Coherent state path integrals are applied to a many-body problem for non-relativistic electrons in a central potential and an external magnetic field; however, in comparison to previous coherent state path integrals, we definitely fix the…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
The derivation of path integrals is reconsidered. It is shown that the expression for the discretized action is not unique, and the path integration domain can be deformed so that at least Gaussian path integrals become probabillistic. This…
Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on an N-dimensional lattice, which is, in most cases, computationally quite the challenging task even with…
Input-output theory is a well-known tool in quantum optics and ubiquitous in the description of quantum systems probed by light. Owing to the generality of the setup it describes, the theory finds application in a wide variety of…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
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…
The Feynman path integral for nonrelativistic quantum electrodynamics is studied mathematically of a standard model in physics, where the electromagnetic potential is assumed to be periodic with respect to a large box and quantized thorough…
After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to…
The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is…
In these lecture notes some applications of Monte Carlo integration methods in Quantum Field Theory - in particular in Quantum Chromodynamics - are introduced and discussed.
We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…
Through a very careful analysis of Dirac's 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {\it The Principles of Quantum Mechanics}, I show that Dirac's contributions to the…