Related papers: Generalized Schrodinger Equation and Constructions…
We have advocated in a previous paper (Godart M. arXiv: 1206.2917v2[quant-ph] ) a version of the stochastic theory of quantum mechanics. It is indirectly based on a method proposed by Nelson to associate a Markov process with any solution…
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…
Any time-dependent solution of Schr\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
From one point of view in the quantum theory of fields, free quantum fields are uniquely determined, not by field equations, but by the transformations of the field and the annihilation and creation operators from which the field is…
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…
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
A generalized version of the creation and annihilation operators is constructed and the factorization of the Schr\"odinger equation is investigated. It is shown that the generalized version of factorization operators yield a factorization…
This paper will describe how combinatorial interpretations can help us understand the algebraic structure of two aspects of perturbative quantum field theory, namely analytic Dyson-Schwinger equations and periods of scalar Feynman graphs.…
Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting vector representation is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum…
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…
We quantize a real massive Klein-Gordon field in curved spacetimes within the general boundary formulation. The vacuum wave function is given by a Gaussian in the Schr\"odinger representation and we study the general structure of the…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent…
A temporally discrete Schroedinger time evolution equation is proposed for isotropic quantum cosmology coupled to a massless scalar source. The approach employs dynamically determined intrinsic time and produces the correct semiclassical…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…