Geometrising the Micro-Cosmos on a Supermanifold
Kieran Finn, Viola Gattus, Sotirios Karamitsos, Apostolos Pilaftsis

TL;DR
This paper explores the extension of the Vilkovisky-DeWitt geometric formalism to supermanifolds, aiming to provide a comprehensive geometric framework for quantum field theories including fermions, with implications for the Standard Model and gravity.
Contribution
It introduces an extension of the Vilkovisky-DeWitt formalism to supermanifolds, addressing fermions and quantum frame dependence in a unified geometric approach.
Findings
Extended VDW effective action to supermanifolds including fermions
Addressed the uniqueness of the path-integral measure in quantum theories
Proposed a geometrisation framework for realistic micro-cosmos theories
Abstract
For more than half a century, covariant and differential geometric methods have been playing a central role in the development of Quantum Field Theory (QFT). After a brief historic overview of the major scientific achievements using these methods, we will focus on the covariant and differential geometric formalism originally proposed by Vilkovisky and DeWitt (VDW). We discuss recent developments made in addressing the uniqueness of the path-integral measure of the VDW effective action, and so address the problem of quantum frame dependence in cosmologically relevant scalar-tensor theories beyond the classical approximation. Particular attention will be drawn to a long-standing problem concerning the obstacles that the VDW formalism was facing from its original conception in describing generic QFTs that include fermions. We show how in addition to bosons the VDW effective action can be…
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Taxonomy
TopicsCosmology and Gravitation Theories · Noncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics
