Related papers: Pathwise Differentiation of Worldline Path Integra…
Accurate long-term predictions of large-scale flow features on planets are crucial for understanding global atmospheric and oceanic systems, necessitating the development of numerical methods that can preserve essential physical structures…
We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an…
We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. Our approach improves upon the proximity force…
A simple method of obtaining path-integral measures in higher-derivative gravities is presented. The measures are nothing but the generalized Lee-Yang terms.
We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…
Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener…
We present a derivation of the Schr\"odinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than what is commonly found in the literature.
This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the…
The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches…
The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid…
The variational autoregressive network is extended to the Euclidean path integral representation of quantum partition function. An essential challenge is adapting the sequential process of sample generation by an autoregressive network to a…
Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path…
A new version of the Casimir effect where the two plates conduct in specific, different, directions is considered. By direct functional integration the evaluation of the Casimir energy as a function of the angle between the conduction…
The method of the factorization of the path integral measure, based on a nonlinear filtering equation, is extended to the case of a nonfree isometric action of the compact semisimple unimodular Lie group on a smooth compact Riemannian…
It is explained how first-quantized worldline path integrals can be used as an efficient alternative to Feynman diagrams in the calculation of QED amplitudes and effective actions. The examples include the one-loop photon splitting…
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…
The calculus of variation and the construction of path integrals is revisited within the framework of non-linear generalized functions. This allows us to make a rigorous analysis of the variation of an action that takes into account the…
We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates…
We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as…