Infinite dimensional analog of the Weil representation in the space of distributions

TL;DR

This paper develops an infinite-dimensional analog of the Weil representation within a new infinite Grassmannian framework, providing a mathematical approach to quantum field theory Schrödinger equations in distribution spaces.

Contribution

It introduces a novel infinite Grassmannian and constructs an infinite-dimensional Weil representation, extending the mathematical tools for quantum field theory.

Findings

Defined a new infinite Grassmannian structure

Constructed an infinite-dimensional Weil representation

Provided solutions to the quantum Schrödinger equation in this framework

Abstract

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 definition of a mathematical solution of the quantum field theory Schr\"odinger equation in the constructed space, and give examples of solutions of this equation.