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Duality and Braiding in Twisted Quantum Field Theory | | Mauro Riccardi
; Richard J. Szabo
; | | Date: |
9 Nov 2007 | | Abstract: | We re-examine various issues surrounding the definition of twisted quantum
field theories on flat noncommutative spaces. We propose an interpretation
based on nonlocal commutative field redefinitions which clarifies previously
observed properties such as the formal equivalence of Green’s functions in the
noncommutative and commutative theories, causality, and the absence of UV/IR
mixing. We use these fields to define the functional integral formulation of
twisted quantum field theory. We exploit techniques from braided tensor algebra
to argue that the twisted Fock space states of these free fields obey
conventional statistics. We support our claims with a detailed analysis of the
modifications induced in the presence of background magnetic fields, which
induces additional twists by magnetic translation operators and alters the
effective noncommutative geometry seen by the twisted quantum fields. When two
such field theories are dual to one another, we demonstrate that only our
braided physical states are covariant under the duality. | | Source: | , 0711.1525 | | Services: | Forum | Review | PDF | Favorites | |
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