Anomalies in gauge theories

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:5010849

Hwang, D S

This thesis consists of various topics of anomalies in two dimensions. Firstly, we study the gauge anomaly. We obtain the solution of the anomaly equation (the Wess-Zumino term) with only gauge fields, without auxiliary fields. We show, up to the second non-trivial order, that this solution agrees with the result of Feynman diagram calculation. By studying the intimate relation between the anomaly and the Schwinger term, we find a method of obtaining the anomaly of D{sub {mu}}J{sup {mu}} (chiral current) from the Schwinger terms of the equal time commutation relations. Through this procedure we can also understand easily the difficulties in quantizing anomalous gauge theories. By studying the Schwinger model, we show that the point-splitting method disagrees with the loop-diagram method by the sign and by the factor 1/2 for the anomaly of {partial derivative}{sub {mu}}J{sub 5}{sup {mu}} and for the Schwinger term of (J{sub 5}{sup 0}(x), J{sup 0}(y)){sub ETC} respectively. Secondly, we study the gravitational anomaly. We calculate Feynman diagrams to get an effective action, and show, up to the second non-trivial order, that this effective action is in agreement with the anomaly obtained by the differential geometric method. Thirdly, we study the supersymmetry anomaly. We obtain a supersymmetric extension of the gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies in the Wess-Zumino gauge. We also find a supermultiplet which contains {partial derivative}{sub {mu}}J{sub 5}{sup {mu}} and {partial derivative}{sub {mu}}J{sup {mu}} as components, and a corresponding anomaly superfield. We confirm this anomaly superfield by diagram calculations.

• Research Organization: California Univ., Berkeley, CA (USA)
• OSTI ID: 5010849
• Country of Publication: United States
• Language: English

Related Subjects

651000* -- Nuclear Physics
657000 -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CALCULATION METHODS
DIAGRAMS
FEYNMAN DIAGRAM
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
SUPERSYMMETRY
SYMMETRY
TWO-DIMENSIONAL CALCULATIONS