On Path Dependent State Space for the Proca Field

TL;DR

This paper revisits a gauge formulation of the Proca quantum theory using an open path functional space, deriving the vacuum state, excited states, and the functional measure for the state space.

Contribution

It introduces a gauge-based path space formulation for the Proca field, including the vacuum, excited states, and the integration measure, advancing the understanding of its quantum structure.

Findings

Derived the path-dependent vacuum state.

Constructed the functional integration measure.

Established a framework for excited states in the path space.

Abstract

A gauge formulation for the Proca model quantum theory in an open path functional space representation is revisited. The path dependent vacuum state is obtained. Starting from this one, other excited states can be obtained too. Additionally, the functional integration measure needed to define an internal product in the state space is constructed.