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.

scholarly journals Canonical ADM tetrad gravity: From metrological inertial gauge variables to dynamical tidal Dirac observables

2015 ◽  
Vol 12 (03) ◽  
pp. 1530001 ◽  
Author(s):  
Luca Lusanna
Keyword(s):  
Particle Physics ◽  
Clock Synchronization ◽  
Canonical Quantization ◽  
Canonical Basis ◽  
Extrinsic Curvature ◽  
Dark Side ◽  
Covariant Formulation ◽  
Poincaré Group ◽  
Poincare Group ◽  
Tetrad Gravity

In this updated review of canonical ADM tetrad gravity in a family of globally hyperbolic asymptotically Minkowskian space-times without super-translations I show which is the status-of-the-art in the search of a canonical basis adapted to the first-class Dirac constraints and of the Dirac observables of general relativity (GR) describing the tidal degrees of freedom of the gravitational field. In these space-times the asymptotic ADM Poincaré group replaces the Poincaré group of particle physics, there is a York canonical basis diagonalizing the York–Lichnerowicz approach and a post-Minkowskian linearization is possible with the associated description of gravitational waves in the family of non-harmonic 3-orthogonal Schwinger time gauges. Moreover I show that every fixation of the inertial gauge variables (i.e. the choice of a non-inertial frame) of every generally covariant formulation of GR is equivalent to a set of conventions for the metrology of the space-time (like the GPS ones near the Earth): for instance the freedom in clock synchronization is described by the inertial gauge variable York time (the trace of the extrinsic curvature of the instantaneous 3-spaces). This inertial gauge freedom and the non-Euclidean nature of the instantaneous 3-spaces required by the equivalence principle are connected with the dark side of the universe and could explain the presence of dark matter or at least part of it by means of the adoption of suitable metrical conventions for the ICRS celestial reference system. Also some comments on a canonical quantization of GR coherent with this viewpoint are done.

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 Bound states in gauge theories as the Poincaré group representations

2013 ◽  
Vol 76 (3) ◽  
pp. 382-396
Author(s):  
A. Yu. Cherny ◽  
A. E. Dorokhov ◽  
Nguyen Suan Han ◽  
V. N. Pervushin ◽  
V. I. Shilin
Keyword(s):  
Bound States ◽  
Gauge Theories ◽  
Poincaré Group ◽  
Group Representations ◽  
Poincare Group

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.

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