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Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motion
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like,…
Functional Schr\"{o}dinger equations for interacting fields are solved via rigorous non-perturbative Feynman type integrals.
In this paper, we investigate the quantum mechanical dynamics of the massive and relativistic Feshbach-Villars oscillator in cosmic dislocation space-time induced by a coulomb-type potential. The first-order Feshbach-Villars version of the…
We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…
The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantum computation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum…
The method of Feynman-Kac perturbation of quantum stochastic processes has a long pedigree, with the theory usually developed within the framework of processes on von Neumann algebras. In this work, the theory of operator spaces is…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate…
Schwinger's quantization scheme is extended in order to solve the problem of the formulation of quantum mechanics on a space with a group structure. The importance of Killing vectors in a quantization scheme is showed. Usage of these…
We present a simple derivation of the Hellmann-Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples which can be used in quantum mechanics lectures: the one-dimensional harmonic…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians. During the past decade, most of…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…
We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time…