Towards non-perturbative quantization and the mass gap problem for the Yang-Mills Field

A. Sevostyanov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we reduce the problem of quantization of the Yang–Mills field Hamiltonian to a problem for defining a probability measure on an infinite-dimensional space of gauge equivalence classes of connections on R3ℝ3. We suggest a formally self-adjoint expression for the quantized Yang–Mills Hamiltonian as an operator on the corresponding Lebesgue L2L2-space. In the case when the Yang–Mills field is associated to the abelian group U(1)U(1), we define the probability measure which depends on two real parameters m>0m>0 and c≠0c≠0. This yields a non-standard quantization of the Hamiltonian of the electromagnetic field, and the associated probability measure is Gaussian. The corresponding quantized Hamiltonian is a self-adjoint operator in a Fock space the spectrum of which is {0}∪[12m,∞){0}∪[12m,∞), i.e. it has a gap.
Original languageEnglish
Article number2150036
Number of pages18
JournalReviews in Mathematical Physics
Volume34
Issue number01
Early online date20 Aug 2021
DOIs
Publication statusPublished - 1 Feb 2022

Keywords

  • Gaussian measure
  • Yang-Mills field

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