Lorentz transformations in relativistic quantum theory?

          @misc{ pirsa_PIRSA:08050031,
            doi = {10.48660/08050031},
            url = {https://pirsa.org/08050031},
            author = {Stefanovich, Eugene},
            keywords = {Cosmology},
            language = {en},
            title = {Lorentz transformations in relativistic quantum theory?},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {may},
            note = {PIRSA:08050031 see, \url{https://pirsa.org}}
          }
          

Abstract

I will review relativistic quantum theory that is based on Wigner\'s unitary representations of the Poincare group, Dirac\'s forms of dynamics, and Newton-Wigner\'s definition of the position operator. Formulas will be derived that transform particle observables between different inertial reference frames. In the absence of interactions, these formulas coincide with Lorentz transformations from special relativity. However, when interaction is turned on, some deviations appear. The relationship of this result to the Currie-Jordan-Sudarshan \'no-interaction\' theorem will be mentioned, and the status of Lorentz transformations within quantum and classical theories of interacting particles will be discussed.