Reduction of Relativistic Wavefunctions to the Irreducible Representations of the Inhomogeneous Lorentz Group. I. Nonzero Mass Components

1967 ◽  
Vol 8 (5) ◽  
pp. 1134-1154 ◽  
Author(s):  
H. E. Moses
Keyword(s):  
Lorentz Group ◽  
Irreducible Representations ◽  
Group I ◽  
Inhomogeneous Lorentz Group

scholarly journals Poincaré Symmetry from Heisenberg’s Uncertainty Relations

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 409 ◽  
Author(s):  
Sibel Başkal ◽  
Young Kim ◽  
Marilyn Noz
Keyword(s):  
Lorentz Group ◽  
Uncertainty Relations ◽  
Quantum Field ◽  
De Sitter ◽  
Sitter Group ◽  
Fundamental Symmetry ◽  
Group I ◽  
Poincaré Symmetry ◽  
Three Space ◽  
Inhomogeneous Lorentz Group

It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the S p ( 2 ) group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the S O ( 2 , 1 ) group. According to Paul A. M. Dirac, from the uncertainty commutation relations for two variables, it possible to construct the de Sitter group S O ( 3 , 2 ) , namely the Lorentz group applicable to three space-like variables and two time-like variables. By contracting one of the time-like variables in S O ( 3 , 2 ) , it is possible to construct the inhomogeneous Lorentz group I S O ( 3 , 1 ) which serves as the fundamental symmetry group for quantum mechanics and quantum field theory in the Lorentz-covariant world. This I S O ( 3 , 1 ) group is commonly known as the Poincaré group.

Canonical representations for massless particles and zero-mass limits of the helicity representation

1965 ◽  
Vol 285 (1401) ◽  
pp. 287-296 ◽  
Keyword(s):  
Lorentz Group ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Positive Mass ◽  
Continuous Spin ◽  
Massless Particles ◽  
Zero Mass ◽  
Canonical Representations ◽  
Inhomogeneous Lorentz Group

The global forms of the unitary irreducible representations of the inhomogeneous Lorentz group corresponding to zero mass and finite or continuous spin are constructed by means of the little-group technique from those of the two-dimensional Euclidean group, and it is shown that these representations may be derived from the helicity representation for positive mass by taking suitable limits.

scholarly journals DERIVATION OF THE SOURCE-FREE MAXWELL AND GRAVITATIONAL RADIATION EQUATIONS BY GROUP THEORETICAL METHODS

2006 ◽  
Vol 15 (04) ◽  
pp. 505-519 ◽  
Author(s):  
JAIRZINHO RAMOS ◽  
ROBERT GILMORE
Keyword(s):  
Lorentz Group ◽  
Gravitational Radiation ◽  
Maxwell Equations ◽  
Free Field ◽  
Flat Space ◽  
Irreducible Representations ◽  
Theoretical Methods ◽  
Covariant Representations ◽  
Divergence Equations ◽  
Inhomogeneous Lorentz Group

We derive source-free Maxwell-like equations in flat space–time for any helicity j by comparing the transformation properties of the 2(2j+1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity j states that carry the irreducible representations of this group. The set of constraints so derived involves a pair of curl equations and a pair of divergence equations. These reduce to the free-field Maxwell equations for j = 1 and the analogous equations coupling the gravito-electric and the gravito-magnetic fields for j = 2.

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