Conjugate variables in quantum field theory and a refinement of Paulis theorem

Steffen Pottel and Klaus Sibold

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Submission date: 04. Mar. 2016
Pages: 38
published in: Physical review / D, 94 (2016) 6, art-no. 065008 
DOI number (of the published article): 10.1103/PhysRevD.94.065008
Bibtex
Keywords and phrases: Quantum Field Theory, Minkowski Space, Conformal Group, polarization
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Abstract:
For the case of spin zero we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors coordinate operators Q conjugate to the momentum operators P exist. The massive case is derived from a geometrical quantity, the massless case is realized by taking the limit m² → 0 on the one hand, on the other from conformal transformations. Crucial is the norm problem of the states on which the Q’s act: they determine eventually how many independent conjugate pairs exist. It is intriguing that (light-) wedge variables and hence the wedge-local case seems to be preferred.