Related papers: Integral transforms of the quantum mechanical path…
Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
I discuss the use of path integrals to study strong-interaction physics from first principles. The underlying theory is cast into path integrals which are evaluated numerically using Monte Carlo methods on a space-time lattice. Examples are…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $\alpha$, called the pathway parameter, one can connect generalized type-1 beta family…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
A new generalization called $\mathtt{k}$-Struve function and its properties given by Nisar and saiful very recently. In this paper, we establish the pathway fractional integral representation of $\mathtt{k}$-Struve function. Many special…
Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce…
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative…
We formulate a new quantum equivalence principle by which a path integral for a particle in a general metric-affine space is obtained from that in a flat space by a non-holonomic coordinate transformation. The new path integral is free of…
We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle…
Using the geometric definition of the topological charge we decompose the path integral of 2-dimensional U(1) lattice gauge theory into topological sectors. In a Monte Carlo simulation we compute the average value of the action as well as…
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct…
We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is…
We formulate Bayesian updates in Markov processes by means of path integral techniques and derive the imaginary-time Schr\"{o}dinger equation with likelihood to direct the inference incorporated as a potential for the posterior probability…
The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral…