Reduction of self-dual yang-mills equations with respect to subgroups of the extended poincaré group

1997 ◽  
Vol 110 (3) ◽  
pp. 329-342
Author(s):  
V. I. Lagno ◽  
V. I. Fushchich
Keyword(s):  
Poincaré Group ◽  
Poincare Group ◽  
Yang Mills

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Roberto Tanzi ◽  
Domenico Giulini
Keyword(s):  
Symplectic Form ◽  
Hamiltonian Formulation ◽  
Hamiltonian Formalism ◽  
Poincaré Group ◽  
Asymptotic Symmetry ◽  
Abelian Gauge ◽  
Poincare Group ◽  
Yang Mills ◽  
Clear Cut ◽  
Asymptotic Symmetries

Abstract We investigate the asymptotic symmetry group of the free SU(N )-Yang-Mills theory using the Hamiltonian formalism. We closely follow the strategy of Henneaux and Troessaert who successfully applied the Hamiltonian formalism to the case of gravity and electrodynamics, thereby deriving the respective asymptotic symmetry groups of these theories from clear-cut first principles. These principles include the minimal assumptions that are necessary to ensure the existence of Hamiltonian structures (phase space, symplectic form, differentiable Hamiltonian) and, in case of Poincaré invariant theories, a canonical action of the Poincaré group. In the first part of the paper we show how these requirements can be met in the non-abelian SU(N )-Yang-Mills case by imposing suitable fall-off and parity conditions on the fields. We observe that these conditions admit neither non-trivial asymptotic symmetries nor non-zero global charges. In the second part of the paper we discuss possible gradual relaxations of these conditions by following the same strategy that Henneaux and Troessaert had employed to remedy a similar situation in the electromagnetic case. Contrary to our expectation and the findings of Henneaux and Troessaert for the abelian case, there seems to be no relaxation that meets the requirements of a Hamiltonian formalism and allows for non-trivial asymptotic symmetries and charges. Non-trivial asymptotic symmetries and charges are only possible if either the Poincaré group fails to act canonically or if the formal expression for the symplectic form diverges, i.e. the form does not exist. This seems to hint at a kind of colour-confinement built into the classical Hamiltonian formulation of non-abelian gauge theories.

scholarly journals Massless finite and infinite spin representations of Poincaré group in six dimensions

2021 ◽  
pp. 136064
Author(s):  
I.L. Buchbinder ◽  
S.A. Fedoruk ◽  
A.P. Isaev ◽  
M.A. Podoinitsyn
Keyword(s):  
Poincaré Group ◽  
Poincare Group ◽  
Six Dimensions ◽  
Spin Representations

scholarly journals Completing Multiparticle Representations of the Poincaré Group

2021 ◽  
Vol 127 (4) ◽  
Author(s):  
Csaba Csáki ◽  
Sungwoo Hong ◽  
Yuri Shirman ◽  
Ofri Telem ◽  
John Terning
Keyword(s):  
Poincaré Group ◽  
Poincare Group

TWISTED POINCARE GROUP AND SPIN-STATISTICS

2005 ◽  
Vol 20 (27) ◽  
pp. 6268-6277 ◽  
Author(s):  
ALEKSANDR PINZUL
Keyword(s):  
Field Theory ◽  
Tensor Product ◽  
Poincaré Group ◽  
Commutative Field ◽  
Poincare Group ◽  
Quantized Fields

Recently it has been shown that it is possible to retain the Lorentz-invariant interpretation of the non-commutative field theory.1,2,3 This was achieved by the means of the twisted action of the Poincaré group on the tensor product of the fields. We investigate the consequences of this approach for the quantized fields.

Quantum Poincaré group

1993 ◽  
Vol 304 (3-4) ◽  
pp. 220-224 ◽  
Author(s):  
M. Chaichian ◽  
A.P. Demichev
Keyword(s):  
Poincaré Group ◽  
Poincare Group
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