Related papers: Star exponentials from propagators and path integr…
This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the…
Inspired by the formalism that relates the star-exponential with the quantum propagator for bosonic systems, in this work we introduce the analogous extension for the fermionic case. In particular, we analyse the problem of calculating the…
We discuss the application of the deformation quantization approach to perturbative quantum field theory. We show that the various forms of Wick's theorem are a direct consequence of the structure of the star products. We derive the…
In this paper, we formulate the phase space description of qubit systems using coadjoint orbits of $SU(2)$ and the Stratonovich-Weyl correspondence, yielding a deformation quantization on the sphere. The resulting star product reproduces…
In this paper, we address the Wigner distribution and the star exponential function for a time-dependent harmonic oscillator for which the mass and the frequency terms are considered explicitly depending on time. To such an end, we explore…
We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology.…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the…
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
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 describe the "Feynman diagram" approach to nonrelativistic quantum mechanics on R^n, with magnetic and potential terms. In particular, for each classical path \gamma connecting points q_0 and q_1 in time t, we define a formal power…
A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory.…
We first rewrite the perturbation expansion of the time evolution operator [An Min Wang, quant-ph/0611216] in a form as concise as possible. Then we derive out the perturbation expansion of the time-dependent complete Green operator and…
It is shown how the pre-exponential factor of the Feynman propagator for a large class of potentials can be computed using contour integrals. This is of direct relevance in the context of tunnelling processes in quantum theories. The…
We study approximations of Feynman path integrals in finite dimensional spaces and how the approximations determine the propagator.
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
Cosmological correlators, the natural observables of the primordial universe, have been extensively studied in the past two decades using the in-in formalism pioneered by Schwinger and Keldysh for the study of dissipative open systems.…