Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

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. In the massive case the notion of interest is derived from a geometrical quantity, the massless case i...

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Bibliographic Details
Published in:Physical review. D 2016-09, Vol.94 (6), Article 065008
Main Authors: Pottel, Steffen, Sibold, Klaus
Format: Article
Language:English
Subjects:
Conformal mapping
Conjugates
Field theory
Operators
Quantum field theory
Quantum theory
Wedges
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Summary: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. In the massive case the notion of interest is derived from a geometrical quantity, the massless case is realized by taking the limit m2→0 on the one hand, on the other, starting with m2=0 directly, from conformal transformations. The norm problem of the states on which the Q’s act is crucial: the states determine eventually how many independent conjugate pairs exist. It is intriguing that (light-) wedge variables and, hence, the wedge-local case seem to be preferred.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.94.065008