Related papers: Dirac and the Path Integral
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…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
In previous papers we have shown how Schr\"{o}dinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field.…
New physical insight into the correspondence between path integral concepts and the Schr\"odinger formulation is gained by the analysis of the effective classical potential, that is defined within the Feynman path integral formulation of…
The path integral formulation of quantum mechanics constructs the propagator by evaluating the action S for all classical paths in coordinate space. A corresponding momentum path integral may also be defined through Fourier transforms in…
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…
Much like the action, diffeomorphism invariance can be used to fix the form of the path integral measure in quantum gravity. Moreover, since there is a redundancy between what constitutes "the action" and what constitutes "the measure" one…
A modern notion of integrability is that of multidimensional consistency (MDC), which classically implies the coexistence of (commuting) dynamical flows in several independent variables for one and the same dependent variable. This property…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
This colloquium summarizes Dirac's contributions to the discovery of quantum mechanics before he invented his relativistic wave equation.
A Lagrangian description of the qubit based on a generalization of Schwinger's picture of Quantum Mechanics using the notion of groupoids is presented. In this formalism a Feynman-like computation of its probability amplitudes is done. The…
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…
Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability…
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and…
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
We analyse two principal approaches to the quantization of physical models worked out to date. There are the Faddeev-Popov "heuristic" approach, based on fixing a gauge in the FP path integrals formalism, and the "fundamental" approach by…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…