Narrow Results

This study addresses a significant gap in the literature by extending the path integral formalism to time-dependent systems within the Wigner–Dunkl framework, deriving exact propagator solutions for analytically solvable cases. By employing generalized canonical transformations, we reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency. Solutions for the Dunkl–Caldirola-Kanai oscillator and a model with a strongly pulsating mass are derived, providing exact propagator expressions and corresponding wave functions. These findings extend the utility of Dunkl operators in quantum mechanics, offering new insights into the dynamics of time-dependent quantum systems and possibly find application in quantum optics, plasma physics, and other fields.

The fermionic one-loop vacuum energy of the superstring theory in a system of non-parallel D1-branes is derived by applying the path integral formalism.

We address the bosonic string pair creation in a system of parallel Dp–Dp′ (p<p′) branes by applying the path integral formalism. We drive the string pair creation rate by calculating the one-loop vacuum amplitude of the setup in the presence of the background electric field defined over the Dp′-brane. It is pointed out that just the components of the electric field defined over the p spatial directions (the common directions along which the both D-branes are extended) give rise to the pair creation.

Using the path integral formalism in (1+1) dimension of the energy–momentum space representation, we calculate the Green function of relativistic spinning particle subjected to the action of combined vector and scalar linear potentials in the framework of deformed Heisenberg algebra which distinguish to the appearance of nonzero minimum position uncertainty given by where β is the deformation parameter of the modified Heisenberg uncertainty relation . We adapt the space–time transformation method to evaluate quantum corrections and this latter are dependent on the α-point discretization interval. The exact bound states spectrum and the corresponding momentum space wave function are obtained.

The relativistic quantum mechanics of the electron in an inhomogeneous magnetic field problem is solved exactly in terms of the momentum space path integral formalism. We adopt the space–time transformation methods, which are $\alpha$-point discretization dependent, to evaluate quantum corrections. The propagator is calculated, the energy eigenvalues and their associated curves are illustrated. The limit case is then deduced for a small parameter.

Recently, H. Benzair et al. [Mod. Phys. Lett. A 35, 2050246 (2020).] formulated in one dimension the nonrelativistic propagator for position-dependent mass (PDM) from the generalized displacement operator approach. According to the path integral formulation, we generalize this process in $D$-dimensional space. As a result, the wave functions are obtained analytically for the pseudo-harmonic oscillator and the inverse square plus Coulomb potentials, and the corresponding energy spectrum are studied. In addition, the effects of PDM on the canonical partition function and other thermodynamic functions have been extracted. The limit cases are then deduced for a small parameter.

In this paper, we study the creation of particles from the vacuum in monolayer graphene by an electromagnetic field in a noncommutative (NC) phase space coordinate considering the Schwinger method. For two different gauges, the probability of particle creation is calculated using the effective action, and special cases are considered. The essential result is that the noncommutativity of the phase space contributes to the effective action and consequently it has an influence on the process of pair creation from the vacuum.

Following the path integral approach and within in the context of nonrelativistic Snyder–de Sitter algebra, we formulate the Green function for Dirac oscillator particle in ($1+1$) space-time dimension. Using the momentum space representation $|p,p_0〉$, we determine the energy eigenvalues and the eigenfunctions, where the wave functions can be given in terms of Gegenbauer polynomials. In addition, the high-temperature thermodynamic properties of the relativistic harmonic oscillators are analyzed, which we found that the heat capacity is not equal two times greater than the heat capacity of the one-dimensional harmonic oscillator for higher temperatures in SdS model. The special cases are found and discussed.

In this paper, the Feynman path integral approach within three parameters Dunkl derivative is investigated in the one-dimensional case of nonrelativistic quantum mechanics. We successfully derive the propagator in Cartesian coordinates and give its exact expression for the free particle, inverse square, harmonic oscillator and pure Coulomb potentials. The energy eigenvalues and their corresponding wave functions are determined.

We propose a simple analytical model for Harmonic oscillator potential that is associated to the generalized uncertainty principle (GUP) in the presence of energy-dependent mass. A formal condition connected with these systems is based on the mathematical structure of modified quantum mechanics. Consequently, thanks to Feynman’s path integrals formalism, we are able to treat the reorganization of wave functions. Furthermore, in order to convert this path formalism into a local representation, we will use a coordinate transformation method at different usual point interval, which is what these systems assume. In each application, the propagator is calculated, the wave functions and the energy eigenvalues are obtained with the corresponding curves. The special cases are then deduced.