相关论文: Hamiltonian path integral quantization in polar co…

Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…

These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…

The harmonic oscillator propagator is found straightforwardly from the free particle propagator, within the imaginary-time Feynman path integral formalism. The derivation presented here is extremely simple, requiring only elementary…

Following the idea of Alekseev and Shatashvili we derive the path integral quantization of a modified relativistic particle action that results in the Feynman propagator of a free field with arbitrary spin. This propagator can be associated…

We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schr\"odinger propagator when the potential is quadratic at infinity. This construction is based on the…

Position-deformed Heisenberg algebra with maximal length uncertainty has recently been proven to induce strong quantum gravitational fields at the Planck scale (2022 J. Phys. A: Math. Theor.55 105303). In the present study, we use the…

We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from…

We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized pulses propagate in anisotropic media.

This paper considers the Schroedinger propagator on a cone with the conical singularity carrying magnetic flux (``flux cone''). Starting from the operator formalism and then combining techniques of path integration in polar coordinates and…

The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a…

The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic…

Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…

In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…

We show how to transform a $d$-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done.…

As long as we neglect backreaction, the Hawking temperature of a given black hole would not depend upon the parameters of the particle species we are considering. In the semiclassical complex path analysis approach of Hawking radiation,…

Recent investigations revealed that the near horizon Hamiltonian of a massless, chargeless outgoing particle, for its particular motion in static as well as stationary black holes, is effectively $\sim xp$ kind. This is unstable by nature…

We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the saddle…

We present a derivation of the Schr\"odinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than what is commonly found in the literature.

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…