Preconjugate variables in quantum field theory and their use
Albert Much, Steffen Pottel, and Klaus Sibold
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Submission date: 04. Mar. 2016
published in: Annals of physics, 94 (2016) 6, art-no. 065007
DOI number (of the published article): 10.1103/PhysRevD.94.065007
with the following different title: Preconjugate variables in quantum field theory and their applications
Keywords and phrases: Quantum Field Theory, Conformal Group, Minkowski Space
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Preconjugate variables X have commutation relations with the energy-momentum P of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new spacetimes we present here a study of them. Interesting examples can be found via geometry: motions on the mass-shell for massive and massless systems, and via group theory: invariance under special conformal transformations of mass-shell, resp. light-cone – both find representations on Fock space. We work mainly in ordinary fourdimensional Minkowski space and spin zero. The limit process from non-zero to vanishing mass turns out to be non-trivial and leads naturally to wedge variables. We point out some applications and extension to more general spacetimes. In a companion paper we discuss the transition to conjugate pairs.