Related papers: Feynman integral in QFT and white noise
The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schr\"odinger equation are…
We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. After sketching this construction for a large class of potentials we show…
In this paper, we consider stochastic Schroedinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are…
The concepts of Feynman integrals in white noise analysis are used to realize the Feynman integrand for a charged particle in a constant magnetic field as a Hida distribution. For this purpose we identify the velocity dependent potential as…
Using the Feynman path integral representation of quantum mechanics it is possible to derive a model of an electron in a random system containing dense and weakly-coupled scatterers, see [Proc. Phys. Soc. 83, 495-496 (1964)]. The main goal…
The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized…
This work is devoted to the causal perturbative Quantum Field Theory (QFT) due to Bogoliubov, including QED and other realistic QFT. It is given the white noise formulation of this theory. The white noise analysis and the Hida operators as…
An effective formalism for white noise analysis, conceptually equivalent to Wilsonian renormalization theory, is introduced. Space-time gets represented by a boolean lattice of coarse regions, energy scales become space-time partitions by…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. We show that the Feynman integrand for the harmonic oscillator in an…
We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schroedinger equation. The Morse potential is considered as a special case.
We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a…
We present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, \emph{i.e.} for a specific momentum, are mathematically interpreted as the Hida operators from the…
We introduce a simple and straight-forward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general…
The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by measures and Laplace transforms of measures, i.e., locally singular as well as rapidly…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the…
We construct Euclidean random fields $X$ over $\R^d$, by convoluting generalized white noise $F$ with some integral kernels $G$, as $X=G* F$. We study properties of Schwinger (or moment) functions of $X$. In particular, we give a general…
In this paper we establish a framework for normal approximation for white noise functionals by Stein's method and Hida calculus. Our work is inspired by that of Nourdin and Peccati (Probab. Theory Relat. Fields 145, 75-118, 2009), who…