Related papers: Pathwise Differentiation of Worldline Path Integra…
The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
We compute the Casimir energy of a real scalar field in the presence of a pair of partially transparent plane mirrors, modeled by Dirac delta potentials.
A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…
This paper introduces the path derivatives, in the spirit of Dupire's functional It\^o calculus, for the controlled paths in the rough path theory with possibly non-geometric rough paths. The theory allows us to deal with rough integration…
We derive a trace formula for the spectra of quantum mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two dimensional hyperboloid. Using this trace formula and the point…
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal,…
Computing the Casimir force and energy between objects is a classical problem of quantum theory going back to the 1940s. Several different approaches have been developed in the literature often based on different physical principles. Most…
I describe a new method for computing trace anomalies in quantum field theories which makes use of path-integrals for particles moving in curved spaces. After presenting the main ideas of the method, I discuss how it is connected to the…
General formalism of quantum field theory and addition theorem for Bessel functions are applied to derive formula for Casimir-Polder energy of interaction between a polarizable particle and a dilute dielectric ball. The equivalence of…
We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in…
We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the $T$-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious…
Vacuum fluctuations of quantum fields between physical objects depend on the shapes, positions, and internal composition of the latter. For objects of arbitrary shapes, even made from idealized materials, the calculation of the associated…
We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by $\delta$-function potentials, so-called semitransparent boundaries. A…
A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well-defined. In particular, it is consistent…
The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one…
The computation of anomalies in quantum field theory may be carried out by evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation of these Jacobians can be cast in the form of a quantum mechanical problem, whose…
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
Rendering algorithms typically integrate light paths over path space. However, integrating over this one unified space is not necessarily the most efficient approach, and we show that partitioning path space and integrating each of these…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…