On Representations of the Lorentz Group
Journal of Advances in Mathematics and Computer Science · pp. 76–82 · Published 28 Apr 2023
10.9734/jamcs/2023/v38i71774Abstract
The Lorentz group is a non-compact group. Consequently, it's representations cannot be expected to be equivalent to representations of a unitary group. Actually, they act on a large-component space and a separated small-component space, in some sense analogous to 4-vectors. In contrast to representations of compact groups state vectors carry the actual value of the non-compact variables, the boost-vector. In the non-boosted state the small components vanish and the large components transform according to a representation of the rotation subgroup. Application of a boost then generates small components, a process that preserves norms. However, the norm now has a growing positive contribution from the large-components and a negative contribution from the small-components, growing absolutely to keep the total unchanged. General transformations are described in detail. The freedom to assign boost directions to the phases of small components leads to a topological symmetry with avor-generating representations for two sheeted representations.
References (8)
- 1 Representation Theory of Semisimple Groups [DOI]
- 2 The Classical Theory of Fields [DOI]
- 3 Modern Particle Physics [DOI]
- 4 Linear Representations of the Lorentz Group [DOI]
- 5 On Unitary Representations of the Inhomogeneous Lorentz Group [DOI]
- 6 Introduction to Elementary Particles 3 [DOI]
- 7 On Quantum Field Theory and Gravitation
- 8 On Generations in Elementary Particle Physics
Cited by 5
Askol'd Mikhailovich Perelomov · Springer eBooks · 1986
Τ. Padmanabhan · Graduate texts in physics · 2016
Sergey Fedoruk, Evgeny Alexeevich Ivanov, J. Lukierski · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 2011
Peter Brands · Symmetry · 2025
Showing 4 of 5 known citations — external sources report more than can currently be individually listed.
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