Nonunitary representations of the Poincaré group and field theory of unstable particles

1969 ◽  
Vol 60 (1) ◽  
pp. 21-39 ◽  
Author(s):  
T. Kawai ◽  
M. Gotō
Keyword(s):  
Field Theory ◽  
Poincaré Group ◽  
Poincare Group ◽  
Unstable Particles

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.

Analytic vectors for the Poincaré group in quantum field theory

1974 ◽  
Vol 15 (2) ◽  
pp. 245-246 ◽  
Author(s):  
Bengt Nagel ◽  
Håkan Snellman
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group

scholarly journals Z0 →2γ AND THE TWISTED COPRODUCT OF THE POINCARÉ GROUP

2007 ◽  
Vol 22 (32) ◽  
pp. 6133-6146 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
S. G. JO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Result ◽  
Invariant Theory ◽  
Massive Particle ◽  
Lepton Number ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group ◽  
Special Case

Yang's theorem forbids the process Z0 →2γ in any Poincaré invariant theory if photons are bosons and their two-particle states transform under the Poincaré group in the standard way (under the standard coproduct of the Poincaré group). This is an important result as it does not depend on the assumptions of quantum field theory. Recent work on noncommutative geometry requires deforming the above coproduct by the Drinfel'd twist. We prove that Z0 →2γ is forbidden for the twisted coproduct as well. This result is also independent of the assumptions of quantum field theory. As an illustration of the use of our general formulae, we further show that Z0 →ν+ ν is forbidden for the standard or twisted coproduct of the Poincaré group if the neutrino is massless, even if lepton number is violated. This is a special case of our general result that a massive particle of spin j cannot decay into two identical massless particles of the same helicity if j is odd, regardless of the coproduct used.

Approach towardsN-nucleon effective generators of the Poincaré group derived from a field theory

1999 ◽  
Vol 59 (4) ◽  
pp. 1919-1929 ◽  
Author(s):  
A. Krüger ◽  
W. Glöckle
Keyword(s):  
Field Theory ◽  
Poincaré Group ◽  
Poincare Group
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