scholarly journals Unitary Representations of the Homogeneous Lorentz Group in an O(1,1)⊗O(2) Basis and Some Applications to Relativistic Equations

1972 ◽  
Vol 13 (9) ◽  
pp. 1304-1312 ◽  
Author(s):  
E. G. Kalnins
Keyword(s):  
Lorentz Group ◽  
Unitary Representations ◽  
Homogeneous Lorentz Group ◽  
Relativistic Equations

Partial-Wave Analysis in Terms of the Homogeneous Lorentz Group

1967 ◽  
Vol 164 (5) ◽  
pp. 1981-1990 ◽  
Author(s):  
R. Delbourgo ◽  
Abdus Salam ◽  
J. Strathdee
Keyword(s):  
Partial Wave ◽  
Lorentz Group ◽  
Partial Wave Analysis ◽  
Wave Analysis ◽  
Homogeneous Lorentz Group

Elements of Group Theory

2021 ◽  
pp. 51-110
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Group Theory ◽  
Lie Groups ◽  
Lorentz Group ◽  
Unitary Representations ◽  
Compact Groups ◽  
Mathematical Language ◽  
Group Representations ◽  
Infinite Groups ◽  
Infinite Dimensional ◽  
Symmetry Properties

The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.

scholarly journals Renormalization of a model for spin-1 matter fields

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Ailier Rivero-Acosta ◽  
Carlos A. Vaquera-Araujo
Keyword(s):  
Lorentz Group ◽  
Homogeneous Lorentz Group ◽  
Mass Dimension ◽  
The One ◽  
Dimension One ◽  
Matter Fields

Abstract In this work, the one-loop renormalization of a theory for fields transforming in the $$(1,0)\oplus (0,1)$$(1,0)⊕(0,1) representation of the Homogeneous Lorentz Group is studied. The model includes an arbitrary gyromagnetic factor and self-interactions of the spin 1 field, which has mass dimension one. The model is shown to be renormalizable for any value of the gyromagnetic factor.

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