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  • Print publication year: 2019
  • Online publication date: June 2019

4 - Matter in the Rest-Frame Instant Form of Dynamics

from Part I - Special Relativity: Minkowski Space-Time


In this chapter there is the description of fields and fluids in the rest-frame instant form of dynamics with the definition of their Wigner-covariant degrees of freedom inside the Wigner 3-spaces after the decoupling of the external center of mass. This is done for the Klein–Gordon, electromagnetic, Dirac, and Yang–Mills fields. In the case of the electromagnetic field there is the identification of the Wigner-covariant Dirac observables. This procedure can be applied also to Yang–Mills fields, but to get the Dirac observables one needs the knowledge of an explicit solution of the Gauss’s law constraints. Then there is the description of relativistic fluids in this framework. In particular a definition of the relativistic micro-canonical ensemble in the Wigner 3-spaces is given and it is shown which equations have to be solved to get a consistent relativistic statistical mechanics.