Related papers: Pathwise Differentiation of Worldline Path Integra…

We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant…

We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (Black-Scholes type) partial differential equation and without explicitly solving the stochastic…

We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational…

The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference…

Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…

We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…

We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…

We present a new Monte Carlo method to calculate Casimir forces acting on objects in a near-critical fluid, considering the two basic cases of a wall and a sphere embedded in a two-dimensional Ising medium. During the simulation, the…

We solve time-sliced path integrals of one-dimensional Coulomb system in an exact manner. In formulating path integrals, we make use of the Duru-Kleinert transformation with Fujikawa's gauge theoretical technique. Feynman kernels in the…

We construct a worldline path integral for the effective action and propagator of a Dirac field in 2+1 dimensions in an Abelian gauge field background. Integrating over an auxiliary gauge group variable we derive a worldline action…

Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…

The standard way to construct a path integral is to use a Legendre transformation to find the hamiltonian, to repeatedly insert complete sets of states into the time-evolution operator, and then to integrate over the momenta. This procedure…

The vacuum expectation value of the stress energy tensor for a massive scalar field with arbitrary coupling in flat spaces with non-trivial topology is discussed. We calculate the Casimir energy in these spaces employing the recently…

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…

A path integral reduction procedure in Wiener-type path integrals, based on the approach developed in arXiv:1912.13124, is applied to a simple invariant mechanical system defined on a product manifold with a given free, proper and isometric…

In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed…