On the universality of the Carter and McLenaghan formula

TL;DR

This paper demonstrates that the Carter and McLenaghan formula for isometry generators in spinor representations is universally applicable across different representations and frames, including natural frames.

Contribution

It establishes the universality of the Carter and McLenaghan formula for isometry generators across all representations and frames, extending its applicability.

Findings

The formula holds for any representation in local and natural frames.

Point-dependent spin matrices are introduced for tensor representations.

Covariant forms of isometry generators are derived in natural frames.

Abstract

It is shown that the formula of the isometry generators of the spinor representation given by Carter and McLenaghan is universal in the sense that this holds for any representation either in local frames or even in natural ones. The point-dependent spin matrices in natural frames are introduced for any tensor representation deriving the covariant form of the isometry generators in these frames.