2012/10/15 by Steven Weinberg · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Curse of dimensionality #Field (mathematics) #Field theory (psychology) #Free field #Invariant (physics) #Lorentz covariance #Lorentz group #Lorentz transformation #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Primary field #Pure mathematics #Quantum mechanics #Representation theory of the Lorentz group #Scale invariance #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.86.105015
14 pages
arxiv created 2012/10/15 · openalex publication_date 2012/11/08 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is shown that in a scale-invariant relativistic field theory, any field \ensuremathψn belonging to the (j,0) or (0,j) representations of the Lorentz group and with dimensionality d=j+1 is a free field. For other field types there is no value of the dimensionality that guarantees that the field is free. Conformal invariance is not used in the proof of these results, but it gives them a special interest; as already known and as shown here in the appendix, the only fields in a conformal field theory that can describe massless particles belong to the (j,0) or (0,j) representations of the Lorentz group and have dimensionality d=j+1. Hence in conformal field theories massless particles are free.