Regular Article - Theoretical Physics
Frame covariant formalism for fermionic theories
Department of Physics and Astronomy, University of Manchester, M13 9PL, Manchester, UK
2 Dipartimento di Fisica, Universitá di Pisa, Pisa, Italy
Accepted: 21 June 2021
Published online: 2 July 2021
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.
© The Author(s) 2021
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