Related papers: Boundary Condition and the Auxiliary Phase in Feyn…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
In the models defined on the inhomogeneous background the propagators depend on the two space - time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations…
It is known that Fourier integral operators arising when solving Schr\"odinger-type operators are bounded on the modulation spaces $\cM^{p,q}$, for $1\leq p=q\leq\infty$, provided their symbols belong to the Sj\"ostrand class…
A contradiction arises when applying standard boundary conditions to a simple quantum rotator with a single coordinate. New boundary conditions for the Schroedinger equation are proposed that involve only gauge invariant quantities, and…
We improve on Cutkosky's cutting rules which is used to calculate the contribution of the singularities of Feynman propagators to Feynman amplitude. The correctness of the improved cutting rules is verified by the calculations of the…
The Kramers problem for quantum fermi-gases with specular - diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers problem the new generalised method of a source of the decision of the boundary problems…
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 study Dirac fields on AdS$_n$ in both global and Poincar\'e charts and, for each mass window, we classify the boundary conditions at conformal infinity that ensure the existence of advanced and retarded propagators. We distinguish the…
We derive an analytical expression for the propagator and the transition path time distribution of a two-dimensional active Brownian particle crossing a parabolic barrier with absorbing boundary conditions at both sides. By taking those of…
Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum…
One-dimensional quantum systems can be experimentally studied in recent nano-technology like the carbon nanotube and the nanowire. We have considered the mathematical model of the one-dimensional Schr\"{o}dinger particle with a junction and…
Invited talk given at the ``International Workshop on `Symmetry Methods in Physics' in memory of Ya.\ A.\ Smorodinsky, 5--10 July 1993, Dubna, Russia; to appear in the proceedings. In this contribution I present further results on steps…
In this paper we provide the DeWitt propagator and its wave function in quantum cosmology using the path integral formulation of quantum gravity. The DeWitt boundary condition is introduced as a way to avoid the Big Bang singularity by…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
Based on the Sum-over-Paths approach of Richard Feynman, an integration method for calculating wave phase vectors is derived. The diffraction and interference patterns of various slit masks can be calculated from such phase vectors. The…
Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational…
We consider the Schrodinger equation with a generalized uncertainty principle for a free particle. We then transform the problem into a second ordinary differential equation and thereby obtain the corresponding propagator. The result of…
I revue the so called Wilson loop approach to bound state problem in QCD. I shall show how using appropriate path integral representations for the quark propagator in an external field it is possible to obtain corresponding path integral…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…