Quantization of multidimensional variational principles
Alexander Roi Stoyanovsky
TL;DR
This paper develops a mathematical framework for quantum field theory by quantizing multidimensional variational principles, leading to algebraic structures that encompass free scalar and conformal fields.
Contribution
It introduces a novel quantization method for classical field observables, connecting variational principles with algebraic quantum field theory.
Findings
Constructs associative algebras from multidimensional variational principles.
Reproduces free algebraic quantum field theory for scalar fields.
Derives free field representations in two-dimensional conformal field theory.
Abstract
We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar field and for the Dirichlet principle, this construction yields free algebraic quantum field theory and free field representation in two dimensional conformal field theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models