Frame Covariant Formalism for Fermionic Theories

Abstract

We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

31 pages, errors due to a mismatch of conventions eliminated

References in corpus (2)

• Frame Covariant Nonminimal Multifield Inflation
• Matching and running sensitivity in non-renormalizable inflationary models

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