Related papers: Path integral formulation of finite-dimensional qu…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and…
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…
The (Feynman) propagator $G(x_2,x_1)$ encodes the entire dynamics of a massive, free scalar field propagating in an arbitrary curved spacetime. The usual procedures for computing the propagator -- either as a time ordered correlator or from…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
The dimension of the Hilbert space of a quantum gravitational system can be written formally as a path integral partition function over Lorentzian metrics. We implement this in a 2+1 dimensional simplicial minisuperspace model in which the…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…
We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…
The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar…
We formulate the coherent state path integral on a two dimensional noncommutative plane using the fact that noncommuative quantum mechanics can be viewed as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on…
Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation…
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…
A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated…