The empirical laws for Majorana fields in a curved spacetime

TL;DR

This paper investigates the empirical laws governing Majorana fields in curved spacetime, addressing the challenge of defining observability in quantum field theory on curved backgrounds.

Contribution

It extends previous work on Klein-Gordon fields to analyze the empirical laws for Majorana fields in curved spacetime, highlighting issues of observability without a vacuum state.

Findings

Examines the concept of empirical laws for Majorana fields in curved spacetime.

Identifies challenges in verifying these laws due to the lack of a vacuum state.

Provides examples illustrating the empirical aspects of Majorana fields in curved backgrounds.

Abstract

This article is a sequel to our previous paper (arXiv:2511.12311), where we considered the conceptual problem on the empirical laws for the Klein\textendash Gordon quantum field theory in curved spacetime (QFTCS), and we will consider the similar problems for the Majorana field on curved spacetime here. A ``law'' in theoretical physics is said to be observable or empirical only if it can be verified/falsified by some experimental procedure. The notion of empiricality/observability becomes far more unclear in QFTCS, than in QFT in Minkowski (flat) spacetime (QFTM), mainly because QFTCS lacks the notion of vacuum. This could potentially undermine the status of QFTCS as a physical (not only mathematical) theory. We consider this problem for the Majorana field in curved spacetime, and examine some examples of the empirical laws.