Related papers: Boundary Condition and the Auxiliary Phase in Feyn…
Starting with a quantum particle on a closed manifold without boundary, we consider the process of generating boundaries by modding out by a group action with fixed points, and we study the emergent quantum dynamics on the quotient…
We study a particle propagation on a circle in the presence of a point interaction. We show that the one-particle Feynman kernel can be written into the sum of reflected and transmitted trajectories which are weighted by the elements of the…
The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
In this paper we show how the transposition, the basic operation of the permutation group, can be taken into account in a diffusion process of identical particles. Whereas in an earlier approach the method was applied to systems in which…
We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original…
We consider boundary element methods where the Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented…
A wide class of boundary problems in quantum mechanics is discussed by using path integrals. This includes motion in half-spaces, radial boxes, rings, and moving boundaries. As a preparation the formalism for the incorporation of…
We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
We present a phase condition under which there is no suitable multiplier for a given continuous-time plant. The condition can be derived from either the duality approach or from the frequency interval approach. The condition has a simple…
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These…
In the first part of our paper we analyze bisolutions and inverses of (non-autonomous) evolution equations. We are mostly interested in pseudo-unitary evolutions on Krein spaces, which naturally arise in linear Quantum Field Theory. We…
We derive and implement a suitable boundary condition for the kinetic description of the electrons inside a plasma, which takes into account microphysical processes inside the wall. It is based on the surface scattering kernel, which…
Recently quantum walks have been considered as a possible fundamental description of the dynamics of relativistic quantum fields. Within this scenario we derive the analytical solution of the Weyl walk in 2+1 dimensions. We present a…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
The problem of the availability of trajectories for the Feynman path integral is considered. Forbidden trajectories for single particle integrals are featured in the case of quantum tunneling across barriers. In the case of multiparticle…
The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…