The role of the irreducible representations of the Poincaré group in solving Maxwell’s equations

2004 ◽  
Vol 45 (5) ◽  
pp. 1887-1918
Author(s):  
Harry E. Moses
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Irreducible Representations ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals ON THE MIXED SYMMETRY IRREDUCIBLE REPRESENTATIONS OF THE POINCARÉ GROUP IN THE BRST APPROACH

2001 ◽  
Vol 16 (11) ◽  
pp. 731-746 ◽  
Author(s):  
ČESTMÍR BURDÍK ◽  
A. PASHNEV ◽  
M. TSULAIA
Keyword(s):  
Weyl Tensor ◽  
Irreducible Representations ◽  
Lagrangian Description ◽  
Verma Modules ◽  
Young Tableaux ◽  
Poincaré Group ◽  
Poincare Group ◽  
Mixed Symmetry

The Lagrangian description of irreducible massless representations of the Poincaré group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is adopted to the systems of second-class constraints by the construction of an auxiliary representations of the algebras of constraints in terms of Verma modules.

scholarly journals SOME FIELD-THEORETICAL ASPECTS OF TWO TYPES OF THE POINCARÉ GROUP REPRESENTATIONS

2014 ◽  
Vol 29 (02) ◽  
pp. 1450020
Author(s):  
L. M. SLAD
Keyword(s):  
Particle Physics ◽  
Irreducible Representations ◽  
Poincaré Group ◽  
Group Representations ◽  
Standard Type ◽  
Poincare Group ◽  
Relativistic Description ◽  
Class Fields ◽  
Infinite Component ◽  
Hadronic States

The capabilities of some approaches to the relativistic description of hadronic states with any rest spin are analysed. The key feature in the Wigner's construction of irreducible representations of the Poincaré group, which makes this construction fruitless in particle physics, is picked out. A realization of unitary irreducible representations of the Poincaré group of the standard type, which has not yet been considered, is discussed. The viability of the description of hadrons by the Poincaré group representations of the standard type in the space of the infinite-component ISFIR-class fields is pointed out.

The irreducible representations of Ũ(12)+

1966 ◽  
Vol 290 (1420) ◽  
pp. 24-43 ◽  
Keyword(s):  
Frame Of Reference ◽  
Irreducible Representations ◽  
Poincaré Group ◽  
Poincare Group ◽  
Infinitesimal Generators ◽  
Physical Representation

The unitary irreducible representations of inhomogeneous Ũ (12) are constructed and a group theoretic basis established for the generalized Bargmann-Wigner equations, introduced by Salam, Delbourgo & Strathdee. All the complications of the problem are concerned with the spacetime transformations which require the generalization of the Poincare group to inhomogeneous Ũ (4). The covariant specification of the Tittle group ’ in terms of the Pauli—Lubanski pseudovector is generalized to Ũ (4), and then to Ũ (12), to give expressions for the infinitesimal generators of the little group which are valid for any physical representation and in any frame of reference.

scholarly journals Chiral symmetry in Dirac equation and its effects on neutrino masses and dark matter

2020 ◽  
Vol 35 (30) ◽  
pp. 2050189
Author(s):  
T. B. Watson ◽  
Z. E. Musielak
Keyword(s):  
Dark Matter ◽  
Dirac Equation ◽  
Chiral Symmetry ◽  
Massive Particle ◽  
Irreducible Representations ◽  
Correct Identification ◽  
Neutrino Masses ◽  
Poincaré Group ◽  
Chiral Angle ◽  
Poincare Group

Chiral symmetry is included into the Dirac equation using the irreducible representations of the Poincaré group. The symmetry introduces the chiral angle that specifies the chiral basis. It is shown that the correct identification of these basis allows explaining small masses of neutrinos and predicting a new candidate for Dark Matter massive particle.

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