2024-03-28T16:24:59Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698902022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Inequivalence of Quantum Dirac Fields of Different Masses and General Structures BehindArai, Asaocanonical anticommutation relationsfermion Fock spaceinequivalent representationmassquantum Dirac eld.410A family of irreducible representations of the canonical anticommutation rela- tions (CAR) over an abstract Hilbert space indexed by a set of bounded linear operators is presented and a theorem on the mutual equivalence of them is estab- lished. As an application of the theorem, it is proved that quantum Dirac elds of different masses are mutually inequivalent. Moreover, a new class of irreducible representations of the CAR over a Hilbert space, which includes, as a special case, time-zero quantum Dirac elds, is constructed.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69890info:doi/10.14943/84230https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69890/1/pre1086.pdfHokkaido University Preprint Series in Mathematics10861202015-12-28engpublisher