104 citations · 249 across the 30 of their papers we have counts for
30 papers
Infinite dimensional analog of the Weil representation in the space of distributions
A. V. Stoyanovsky
We construct a new version of infinite Grassmannian and infinite dimensional analog of the Weil representation of the affine symplectic group in the space of distributions. We give…
Generalizations of wave equations to multidimensional variational problems
A. V. Stoyanovsky
This is a survey paper based on previous results of the author. In the paper, we define and discuss the generalizations of linear partial differential equations to multidimensional…
Mathematical renormalization of Hamiltonian field theories
A. V. Stoyanovsky
We rigorously define renormalized evolution operator of the Schrödinger equation in the infinite dimensional Weyl-Moyal algebra for any time interval for arbitrary Hamiltonian depe…
A new mathematical problem related to quantization of fields
A. V. Stoyanovsky
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
Differential operators on infinite dimensional space and quantum field theory
A. V. Stoyanovsky
We conjecture that the renormalized perturbative -matrix of quantum field theory coincides with the evolution operator of the standard functional differential Schrodinger equati…
A-hypergeometric functions in transcendental questions of algebraic geometry
A. V. Stoyanovsky
We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are…