Quantum field theory on a seven‐dimensional homogeneous space of the Poincaré group

1974 ◽  
Vol 15 (7) ◽  
pp. 1007-1024 ◽  
Author(s):  
C. P. Boyer ◽  
G. N. Fleming
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Homogeneous Space ◽  
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.

scholarly journals Supersymmetry: Early Roots That Did Not Grow

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Cecilia Jarlskog
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group

This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

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