Related papers: Feynman Equation in Hamiltonian Quantum Field Theo…
Schr\"{o}dinger equations in \emph{functional derivatives} are solved via quantized Galerkin limit of antinormal functional Feynman integrals for Schr\"{o}dinger equations in \emph{partial derivatives
We consider functional Schr\"{o}dinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock…
In these lectures we introduce the Feynman-Schwinger representation method for solving nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving…
Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to…
The generalized Schrodinger equation deduced in the earlier papers is compared with conventional constructions of quantum field theory. In particular, it yields the usual Schrodinger equation of quantum field theory written without normal…
A Feynman path integral formula for the Schr\"odinger equation with magnetic field is rigorously mathematically realized in terms of infinite dimensional oscillatory integrals. We show (by the example of a linear vector potential) that the…
The equivalence of two formulations of Fokker's quantum theory is proved - based on the Feynman functional integral representation of the propagator for a system of charges with direct electromagnetic interaction and the quantum principle…
By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose…
In this paper, the massless Schwinger model or two dimensional quantum electrodynamics is exactly solved on a Riemann surface. The partition function and the generating functional of the correlation functions involving the fermionic…
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum…
A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of $n$-fold iterated…
The fundamental solution of the Schr\"odinger equation for a free particle is a distribution. This distribution can be approximated by a sequence of smooth functions. It is defined for each one of these functions, a complex measure on the…
Single scale Feynman integrals in quantum field theories obey difference or differential equations with respect to their discrete parameter $N$ or continuous parameter $x$. The analysis of these equations reveals to which order they…
At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
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…
New types of relationships between Feynman integrals are presented. It is shown that Feynman integrals satisfy functional equations connecting integrals with different values of scalar invariants and masses. A method is proposed for…
We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schr\"odinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves…
In this paper we consider the simplest functional Schroedinger equation of a quantum field theory (in particular QCD) and study its solutions. We observe that the solutions to this equation must possess a number of properties. Its Taylor…