On the geometry of ghosts

TL;DR

This paper explores the geometric foundations of quantum gauge theories, proposing a unified scheme for constructing quantum fields and their conjugates, with particular focus on ghosts, antifields, and BRST symmetry.

Contribution

It introduces a geometric approach to quantum gauge fields, clarifying the role of ghosts and antifields within a unified framework based on Fr"olicher-smooth bundles.

Findings

A general rule for constructing quantum fields and conjugates.

Insights into the geometric nature of ghosts and antifields.

Relation between antifields and BRST symmetry clarified.

Abstract

An inspection of the precise geometric constructions underlying fundamental notions in quantum gauge field theories sheds light on various aspects which tend to be obscured in the usual formalisms. Revising the notions of mutually conjugated "internal" bundles we propose a general rule for the constructions of free quantum fields and their conjugates, naturally yielding the needed fundamental properties with regard to contractions, super-commutators, field momentum and Hamiltonian, and other quantities. This scheme applies to fields of all types; in particular we examine consequences in relation to ghosts and anti-ghosts. Finally in the context of observer-independent Fr\"olicher-smooth quantum bundles we show how the antifield sectors naturally arise, and examine the precise relation among these and the BRST symmetry of a gauge field theory.