Review and concrete description of the irreducible unitary representations of the universal cover of the complexified Poincaré group
Articolo
Data di Pubblicazione:
2023
Citazione:
Review and concrete description of the irreducible unitary representations of the universal cover of the complexified Poincaré group / L.M. Borasi. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - 35:1(2023 Feb), pp. 2230004.1-2230004.28. [10.1142/S0129055X22300047]
Abstract:
In this paper, we give a pedagogical presentation of the irreducible unitary representations of 4 Spin(4, ), that is, of the universal cover of the complexified Poincaré group 4 SO(4, ). 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 4 Spin0(1, 3). Our analysis is motivated by the interest in the Euclidean formulation of Fermionic theories.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Poincaré group; complexification; Wigner–Mackey theory; relativistic quantum field theory; unitary representation; semisimple Lie group;
Elenco autori:
L.M. Borasi
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