# Ghostbusters: Unitarity and Causality of Non-equilibrium Effective Field Theories

## TL;DR

This paper proves that non-equilibrium effective field theories along a closed time path inherently satisfy causality and unitarity constraints if their propagators have the correct pole structure, without requiring ghost fields or BRST symmetry.

## Contribution

It provides a simple proof that the largest time equation holds at all loop orders under certain propagator conditions, clarifying foundational aspects of non-equilibrium EFTs.

## Key findings

- Largest time equation holds at all loop orders with proper propagator poles
- Ghost fields are unnecessary as their contributions vanish
- Ensures causality and unitarity in non-equilibrium EFTs

## Abstract

For a non-equilibrium physical system defined along a closed time path (CTP), a key constraint is the so-called largest time equation, which is a consequence of unitarity and implies causality. In this paper, we present a simple proof that if the propagators of a non-equilibrium effective action have the proper pole structure, the largest time equation is obeyed to all loop orders. Ghost fields and BRST symmetry are not needed. In particular, the arguments for the proof can also be used to show that if ghost fields are introduced, their contributions vanish.