Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Review and concrete description of the irreducible unitary representations of the universal cover of the complexified Poincaré group (2108.10726v1)

Published 24 Aug 2021 in math-ph, math.MP, and quant-ph

Abstract: We give a pedagogical presentation of the irreducible unitary representations of $\mathbb{C}4\rtimes\mathbf{Spin}(4,\mathbb{C})$, that is, of the universal cover of the complexified Poincar\'e group $\mathbb{C}4\rtimes\mathbf{SO}(4,\mathbb{C})$. These representations were first investigated by Roffman in 1967. We provide a modern formulation of his results together with some facts from the general Wigner-Mackey theory which are relevant in this context. Moreover, we discuss different ways to realize these representations and, in the case of a non-zero "complex mass", we give a detailed construction of a more explicit realization. This explicit realization parallels and extends the one used in the classical Wigner case of $\mathbb{R}4\rtimes\mathbf{Spin}0(1,3)$. Our analysis is motivated by the interest in the Euclidean formulation of Fermionic theories.

Summary

We haven't generated a summary for this paper yet.