Related papers: Path Integral Approach to 't Hooft's Derivation of…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
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…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
We develop a two-dimensional gravity path integral formulation of the $T \bar T + \Lambda_2$ deformation of quantum field theory. This provides an exactly solvable generalization of the pure $T \bar T$ deformation that is relevant for de…
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path…
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The algebraic approach to quantum mechanics has been vital to the development of quantum theory since its inception, and it has evolved into a mathematically rigorous $C^\ast$-algebraic formulation of the theory's axioms. Conversely, the…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
It is shown that for any given quantum system evolving unitarily with the Hamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote $D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smooth potential…
Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase…
We study the heat statistics of a quantum Brownian motion described by the Caldeira-Leggett model. By using the path integral approach, we introduce a novel concept of the quantum heat functional along every pair of Feynman paths. This…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
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…
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in "natural form",…
It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics.…
A closed (in terms of classical data) expression for a transition amplitude between two generalized coherent states associated with a semisimple Lee algebra underlying the system is derived for large values of the representation highest…