Weinberg-Witten theorem
The Weinberg-Witten theorem , after Steven Weinberg and Edward Witten , is a statement in quantum field theory . Under very general assumptions, it derives exclusion criteria for the properties of particles. This makes the Weinberg-Witten theorem one of the so-called no-go theorems in quantum field theory. The Weinberg-Witten theorem links the maximum spin of a massless particle with its transported charge , assuming the validity of Einstein's special theory of relativity . The most important consequence of the Weinberg-Witten theorem is that the graviton , if it exists, must be an elementary particle .
The Weinberg-Witten theorem specifically states the following:
- In theories with a Lorentz covariant energy-momentum tensor , massless particles with a spin are forbidden.
- In theories with a preserved symmetry , and if the symmetry on which the charge is based is a gauge symmetry, a gauge- invariant charge and a Lorentz covariant current, massless particles with a spin that carry such a charge are forbidden.
The union of the general relativity theory with the quantum field theory in the context of a quantum field theory on curved spacetime with its standard graviton is not affected by the Weinberg-Witten theorem, since its energy-momentum tensor is not Lorentz covariant. However, it rules out all theories with massless gravitons built from Standard Model or SUSY particles.
Likewise, neither Abelian nor non - Abelian Yang-Mills theories , on which the Standard Model is based, are affected, since Abelian theories such as quantum electrodynamics only lead to uncharged particles with spin and non- Abelian theories such as quantum chromodynamics have no gauge invariant Noether charges.
The Weinberg-Witten theorem does not make a statement for massive particles.
literature
- Steven Weinberg and Edward Witten: Limits on Massless Particles . In: Phys. Lett. B. Band 96 , no. 1-2 , 1980, pp. 59-62 , doi : 10.1016 / 0370-2693 (80) 90212-9 (English).