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NoGo Theorem for “Free” Relativistic Anyons in d=2+1”, FUBerlin preprint
"... We show that a quantum field theoretic model of anyons cannot be “free ” in the (restrictive) sense that the basic fields create only oneparticle states out of the vacuum. Mathematics Subject Classification (1991): 81T05, 32A10. Keywords: Abelian braid group statistics, JostSchroer theorem, free f ..."
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We show that a quantum field theoretic model of anyons cannot be “free ” in the (restrictive) sense that the basic fields create only oneparticle states out of the vacuum. Mathematics Subject Classification (1991): 81T05, 32A10. Keywords: Abelian braid group statistics, JostSchroer theorem, free field.
Notes on Wigner’s Representation Theory of the Poincaré Group, Localization and Statistics
"... It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbertspace. This ”modular localization ” is not only useful in order to construct interactionfree nets of local al ..."
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Cited by 10 (2 self)
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It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbertspace. This ”modular localization ” is not only useful in order to construct interactionfree nets of local algebras without using nonunique ”free field coordinates”, but also permits the study of properties of localization and braidgroup statistics in lowdimensional QFT. It also sheds some light on the stringlike localization properties of the 1939 Wigner’s ”continuous spin ” representations.We formulate a constructive nonperturbative program to introduce interactions into such an approach based on the TomitaTakesaki modular theory. The new aspect is the deep relation of the latter with the scattering operator. 1 Introduction. The main aim of this paper is the exploration and extension of Wigner’s
Wigner Representation Theory of the Poincar'e Group, Localization , Statistics and the SMatrix
 Phys. B
"... It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbertspace. This "modular localization" is not only useful in order to construct interactionfree nets of ..."
Abstract
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It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbertspace. This "modular localization" is not only useful in order to construct interactionfree nets of local algebras without using nonunique "free field coordinates ", but also permits the study of properties of localization and braidgroup statistics in lowdimensional QFT. It also sheds some light on the stringlike localization properties of the 1939 Wigner's "continuous spin" representations. We formulate a constructive nonperturbative program to introduce interactions into such an approach based on the TomitaTakesaki modular theory. The new aspect is the deep relation of the latter with the scattering operator. 1 Introduction. The main aim of this paper is the exploration and extension of Wigner's representationtheoretic approach to relativistic quantum theory [1] for the construction of p...