TY - JOUR

T1 - Anomaly cancellation in extended phase space. The chiral Schwinger model

AU - Moshe, Moshe

AU - Oz, Yaron

N1 - Funding Information:
¢~ Work supported in part by the Israeli Academy of Science - Fund for Basic research, the US-Israel Binational Science Foundation, by the fund for the promotion of research at the Technion and the Lawrence Deutsch Research Fund. ~ Here the method of Batalin and Fradkin has been considered for the quantization of the zero mode of the superstring where the mixing of first-and second-class constraints prevent a straightforward covariant quantization. See also ref. \[1 2 \] where the first-and second-class constraints are treated in a symmetrical fashion in the case of the massive superparticle and the relation between the Batalin-Fradkin extended phase space and Stueckelberg's approach in the case of a massive vector boson are thoroughly studied.

PY - 1989/6/22

Y1 - 1989/6/22

N2 - Quantum mechanically broken symmetries can be restored by properly extending the initial phase space to include extra degrees of freedom. The chiral Schwinger model is an ideal example in which general methods for restoration of a quantum mechanically broken symmetry can be studied. Here we construct an extended phase space, following recent ideas of Batalin and Fradkin in which quantum mechanically induced second-class constraints in the original system are made first class in the corresponding symmetric system. In the extended phase space, the anomalous theory can be viewed as a gauge fixed (a "unitary gauge") version of the new symmetric theory. Once this corresponding symmetric theory is determined, one can exploit the restored gauge symmetry and the freedom of fixing the gauge. Different gauges can be employed which reflect different physical aspects of the theory in a more transparent way than in the original gauge fixed (anomalous) theory. The particular restoration of symmetry used here is compared to the more conventional approach of adding a Wess-Zumino term to the action or adding extra right-handed fermions.

AB - Quantum mechanically broken symmetries can be restored by properly extending the initial phase space to include extra degrees of freedom. The chiral Schwinger model is an ideal example in which general methods for restoration of a quantum mechanically broken symmetry can be studied. Here we construct an extended phase space, following recent ideas of Batalin and Fradkin in which quantum mechanically induced second-class constraints in the original system are made first class in the corresponding symmetric system. In the extended phase space, the anomalous theory can be viewed as a gauge fixed (a "unitary gauge") version of the new symmetric theory. Once this corresponding symmetric theory is determined, one can exploit the restored gauge symmetry and the freedom of fixing the gauge. Different gauges can be employed which reflect different physical aspects of the theory in a more transparent way than in the original gauge fixed (anomalous) theory. The particular restoration of symmetry used here is compared to the more conventional approach of adding a Wess-Zumino term to the action or adding extra right-handed fermions.

UR - http://www.scopus.com/inward/record.url?scp=0001368820&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(89)91065-4

DO - 10.1016/0370-2693(89)91065-4

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AN - SCOPUS:0001368820

SN - 0370-2693

VL - 224

SP - 145

EP - 152

JO - Physics Letters B

JF - Physics Letters B

IS - 1-2

ER -