The impossible regularization of the Nambu Jona-Lasinio model with vector interactions

Details The impossible regularization of the Nambu Jona-Lasinio model with vector interactions The impossible regularization of the Nambu Jona-Lasinio model with vector interactions

1996-05-23

arxiv.org/abs/hep-ph/9605381v1

Nucl.Phys. A606 (1996) 292-302

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages in Latex, available from ripka@amoco.saclay.cea.fr

Scientific paper

10.1016/0375-9474(96)00204-7

We show that the procedure of regularizing the real part of the euclidean action, while leaving the imaginary part unregularized, leads to a non-analytic and highly singular functional of the fields. It is customary to work with an imaginary time component of the vector field, in order to avoid regularization of the anomalous processes. We show that this procedure is flawed by the fact that a stationary point of the action occurs for a real, not imaginary, time component of the vector field. Furthermore the action in the vicinity of the stationary point is singular. The regularized action is thus not suitable for an evaluation of the partition function using a saddle point method. We discuss proposed solutions to this problem, as well as other regularizations. They all lead to practical problems.

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