Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

Details Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

2000-10-11

arxiv.org/abs/hep-th/0010080v1

Annals Phys. 296 (2002) 98-127

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, Revtex

Scientific paper

10.1006/aphy.2001.6214

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In the $QED_2$ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In the anomalous chiral $QED_2$ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of $\theta$-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.

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