Extensions of the Poincare group

TL;DR

This paper constructs an extended superPoincare group with infinite generators mixing internal and space-time supersymmetries, explores its representations, and suggests a similar extension for the conformal group.

Contribution

It introduces a novel infinite-dimensional extension of the superPoincare group with explicit matrix representations and analyzes its massless irreducible representations.

Findings

Infinite series of helicities in transversal representations

Explicit matrix representations of the extended group

Proposed extension of the conformal group

Abstract

We construct an extension of the Poincare group which involves a mixture of internal and space-time supersymmetries. The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and space-time indices. It is a closed algebra since all Jacobi identities are satisfied and it has therefore explicit matrix representations. We investigate the massless case and construct the irreducible representations of the extended symmetry. They are divided into two sets, longitudinal and transversal representations. The transversal representations involve an infinite series of integer and half-integer helicities. Finally we suggest an extension of the conformal group along the same line.