The discussion centers around the requirement of locality in quantum field theory (QFT), exploring its implications for the Lagrangian density and the interactions between fields. Participants examine the foundational concepts of locality, the cluster decomposition property, and the consequences for causality and interactions in QFT.
Participants express differing views on the implications and definitions of locality, with no consensus reached on the necessity or interpretation of locality in QFT. The discussion remains unresolved regarding the precise relationship between locality, causality, and the structure of the Lagrangian density.
Some participants reference the need for further study of specific texts, such as Weinberg's work, to deepen understanding of the concepts discussed. There are indications of missing assumptions and unresolved mathematical steps related to the implications of locality.
Would this also be true for a non-compact gauge group?vanhees71 said:I think what Schwartz discusses there is the realization of an Abelian massive vector field as a gauge field. This is a remarkable model, because it shows that in the Abelian case, i.e., gauge group U(1), you can formulate a gauge-symmetric renormalizable model with massive gauge bosons without the Higgs mechanism. This construct does not work for the non-Abelian case. There you need the Higgs mechanism to consistently describe massive gauge bosons and/or fermions for chiral gauge groups as in the electroweak sector of the Standard Model.