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 language | English |
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Article number | 2150036 |
Number of pages | 18 |
Journal | Reviews in Mathematical Physics |
Volume | 34 |
Issue number | 01 |
Early online date | 20 Aug 2021 |
DOIs | |
Publication status | Published - 1 Feb 2022 |
Keywords
- Gaussian measure
- Yang-Mills field