Related papers: Non-standard phase space variables, quantization, …
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
A path integral representation is given for the solutions of the 3+1 dimensional Dirac equation. The regularity of the trajectories, the non-relativistic limit and the semiclassical approximation are briefly mentioned.
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…
This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe…
Whenever variables $\phi=(\phi^1,\phi^2,\ldots)$ are discarded from a system, and the discarded information capacity $\mathcal{S}(x)$ depends on the value of an observable $x$, a quantum correction $\Delta V_\mathrm{eff}(x)$ appears in the…
I study several aspects of the path(st) integral we formulated in previous papers on energetic causal sets with Cortes and others. The focus here is on quantum field theories, including the standard model of particle physics. I show that…
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…
The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…
We axiomatize path integral quantization of symplectic manifolds. We prove that this path integral formulation of quantization is equivalent to an abstract operator formulation, ie. abstract coherent state (or Berezin) quantization. We use…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
Phase space quasi-probability functions provide powerful representations of quantum states and operators, as well as criteria for assessing quantum computational resources. In discrete, odd-dimensional systems (qudits), protocols involving…
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…
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…
The normalization in the path integral approach to quantum field theory, in contrast with statistical field theory, can contain physical information. The main claim of this paper is that the inner product on the space of field…
Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
The review considers statistical systems composed of several phases that are intermixed in space at mesoscopic scale and systems representing a mixture of several components of microscopic objects. These types of mixtures should be…