Covariant actions and propagators for all spins, masses, and dimensions

The explicit covariant actions and propagators are given for fields describing particles of all spins and masses, in any spacetime dimension. Massive particles are realized as “dimensionally reduced” massless particles. To obtain compact expressions for the propagators, it was useful to introduce an auxiliary vector coordinate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>s</a:mi><a:mi>μ</a:mi></a:msup></a:math> and consider “hyperfields” that are functions of space <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>X</c:mi><c:mi>μ</c:mi></c:msup></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>s</e:mi><e:mi>μ</e:mi></e:msup></e:math>. The actions and propagators serve as a basic starting point for concrete high spin computations amenable to dimensional regularization, provided that gauge invariant interactions are introduced. Published by the American Physical Society 2024