scholarly journals Propagation of a relativistic particle in terms of the unitary irreducible representations of the Lorentz group

2001 ◽  
Vol 22 (3) ◽  
pp. 581-584 ◽  
Author(s):  
R.A. Frick
Keyword(s):  
Lorentz Group ◽  
Relativistic Particle ◽  
Irreducible Representations

The Duflo non-commutative Fourier transform for the Lorentz group

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040011
Author(s):  
Giacomo Rosati
Keyword(s):  
Fourier Transform ◽  
Phase Space ◽  
Quantum System ◽  
Lie Group ◽  
Lorentz Group ◽  
Commutative Algebra ◽  
Cotangent Bundle ◽  
Irreducible Representations ◽  
Algebra Representation

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

On the irreducible representations of the lorentz group

1976 ◽  
Vol 99 (1) ◽  
pp. 92-126 ◽  
Author(s):  
Seán Browne ◽  
Djordje Šijački
Keyword(s):  
Lorentz Group ◽  
Irreducible Representations

On particle-like representations of the complete homogeneous Lorentz group

1973 ◽  
Vol 74 (1) ◽  
pp. 149-160 ◽  
Author(s):  
J. A. de Wet
Keyword(s):  
Lorentz Group ◽  
Wave Functions ◽  
Unitary Groups ◽  
Irreducible Representations ◽  
Electron Wave ◽  
Precise Form ◽  
Homogeneous Lorentz Group ◽  
The Many ◽  
Matrix Contraction

In two previous papers (1, 2) representations of the unitary groups U4, U2 were found which described some of the properties of nucleons and electrons. In particular, the many electron wave functions were constructed from the irreducible representations of U2 restricted to the proper orthochronous Lorentz group Lp. In this paper the irreducible representations of U4 found in (1) will be shown to be also irreducible representations of the complete homogeneous Lorentz group L0 and the techniques of matrix contraction employed in (2) will be used to find the precise form of the matrices of the infinitesimal ring.

Relativistic symmetry

2021 ◽  
pp. 8-30
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Group Theory ◽  
Lorentz Group ◽  
Irreducible Representations ◽  
Lorentz Transformations ◽  
Not Given ◽  
Poincare Group ◽  
Relativistic Symmetry ◽  
Tensor Representations ◽  
The Subject ◽  
Spinor Representations

This chapter discusses relativistic symmetry, starting from the Lorentz transformations. Basic notions of group theory are introduced before a more detailed discussion of the Lorentz and Poincaré groups is given. Tensor representations and spinor representations of the Lorentz group are described, although full proofs of the theorems are not given. The chapter ends with the irreducible representations of the Poincaré group. This chapter provides all of the necessary notions for group theory, although it is not intended to replace a textbook on the subject.

Sign in / Sign up

Export Citation Format

Share Document