TY - JOUR

T1 - Currents in anomalous gauge theories

AU - Harada, Koji

N1 - Funding Information:
Anomalous gauge theories (AGT's) are systems with second-class constraints in the quantum-mechanical sense. Faddeev \[1\]r ecognized that the Gauss law constraint in the AGT is second-class. On the other hand, Jackiw and Rajaraman \[2\] considered the chiral Schwinger model (chiral QED2) and showed that it is consistent and unitary. More strictly speaking, it is shown that the chiral Schwinger model can be quantized consistently as a system with second-class constraints and unitary for a certain region of a regularization parameter \[3,4 \]. It is very useful to analyze the bosonized models (in two dimensions) \[5,6\] because quantum-mechanical second-class constraints appear in the tree level in those bosonized models. It is therefore natural that several authors considered non-linear sigma models as (low-energy) effective theories of AGT's in four dimensions \[7\]. Generally speaking, AGT's may have more degrees of freedom than the usual normal theories have. There are two approaches to deal with these additional degrees of freedom. In the first approach, sometimes called the "gauge non-invariant formulation", we integrate gauge fields over entire configuration space in the path integral. In the case of the (bosonized) chiral Schwinger model, we have the * This work is partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (63790159). ** JPSP fellow. Address after 1 April 1989: Institut fiir Theoretische Physik der Universitiit Heidelberg, FRG.

PY - 1990/1/15

Y1 - 1990/1/15

N2 - Anomalous gauge theories are considered in the gauge invariant and the gauge non-invariant formulations. We show that the currents which couple to gauge fields are conserved in both formulations. Equal-time commutators for the fermion charge density [(JL0)a(x),(JL0)b(y)]ET are calculated explicitly in the bosonized chiral QCD2. We emphasize the usefulness of the gauge invariant formulation.

AB - Anomalous gauge theories are considered in the gauge invariant and the gauge non-invariant formulations. We show that the currents which couple to gauge fields are conserved in both formulations. Equal-time commutators for the fermion charge density [(JL0)a(x),(JL0)b(y)]ET are calculated explicitly in the bosonized chiral QCD2. We emphasize the usefulness of the gauge invariant formulation.

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U2 - 10.1016/0550-3213(90)90079-S

DO - 10.1016/0550-3213(90)90079-S

M3 - Article

AN - SCOPUS:0038873106

VL - 329

SP - 723

EP - 738

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -