Question

I am studying the Fujikawa method of determining the chiral anomalies in a U(1)

theory. As we know the basis vectors selected are the eigenstates of the Dirac operator. One of the reasons given is that the eigenstates diagonalize the action which is needed for determining an exact quantity such as Ward-Takahashi identities. Anyone care to explain?

Answer 1

The Fujikawa method is used to determine chiral anomalies in a U(1) theory. The eigenstates of the Dirac operator are chosen as basis vectors because they diagonalize the action, making it easier to analyze and calculate exact quantities like Ward-Takahashi identities.

Step-by-step explanation:

The Fujikawa method is used to determine chiral anomalies in a U(1) theory. The basis vectors selected in this method are the eigenstates of the Dirac operator. One reason for choosing these eigenstates is that they diagonalize the action, which is important for determining exact quantities like Ward-Takahashi identities.

When the action is diagonalized, it becomes easier to analyze and calculate various properties of the system. The eigenstates of the Dirac operator provide a convenient basis in which to study the chiral anomalies because they simplify the theoretical calculations involved.