Generalization of the Coleman-Mandula Theorem to Higher Dimension

TL;DR

This paper extends the Coleman-Mandula theorem to higher-dimensional spacetimes using a rigorous Dirac formalism, exploring potential further generalizations and demonstrating the formalism's practical utility.

Contribution

It provides a mathematically rigorous proof of the Coleman-Mandula theorem in higher dimensions, incorporating advanced distribution theory.

Findings

The theorem is valid in higher spacelike dimensions.

The proof utilizes a rigorous Dirac formalism based on distributions.

Potential for further generalizations is discussed.

Abstract

The Coleman-Mandula theorem, which states that space-time and internal symmetries cannot be combined in any but a trivial way, is generalized to an arbitrarily higher spacelike dimension. Prospects for further generalizations of the theorem (space-like representations, larger time-like dimension, infinite number of particle types) are also discussed. The original proof relied heavily on the Dirac formalism, which was not well defined mathematically at that time. The proof given here is based on the rigorous version of the Dirac formalism, based on the theory of distributions. This work serves also to demonstrate the suitability of this formalism for practical applications.