An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

作者：Kumar R^*; Gupta S; Malik R P

来源：Communications in Theoretical Physics, 2014, 61(6): 715-728.

DOI：10.1088/0253-6102/61/6/10

• continuous symmetries
• 2D QED with fermionic Dirac fields
• symmetry principles
• basic canonical (anti)commutators
• creation and annihilation operators
• conserved charges as generators
• de Rham cohomological operators
• Hodge theory

We derive the basic canonical brackets amongst the creation and annihilation operators for a two (1 + 1)-dimensional (2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field (A(mu)) is coupled with the fermionic Dirac fields (psi and (psi) over bar). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries (and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta (corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries (and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.

• 出版日期2014-6