Related papers: A note on the Stochastic nature of Feynman quantum…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
We connect the weak measurements framework to the path integral formulation of quantum mechanics. We show how Feynman propagators can in principle be experimentally inferred from weak value measurements. We also obtain expressions for weak…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out…
In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the…
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…
We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…
In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter $H<1/2$. To establish such a…
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…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
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…
A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory.…
We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
We investigate conditional McKean-Vlasov equations driven by time-space white noise, motivated by the propagation of chaos in an N-particle system with space-time Ornstein-Uhlenbeck dynamics. The framework builds on the stochastic calculus…
We study the quantization problem of relativistic scalar and spinning particles interacting with a radiation electromagnetic field by using the path integral and the external source method. The spin degrees of freedom are described in terms…
We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…