Massless scalar free Field in 1+1 dimensions I: Weyl algebras Products and Superselection Sectors

Abstract

This is the first of two papers on the superselection sectors of the conformal model in the title, in a time zero formulation. A classification of the sectors of the net of observables as restrictions of solitonic (twisted) and non-solitonic (untwisted) sector automorphisms of proper extensions of the observable net is given. All of them are implemented by the elements of a field net in a non-regular vacuum representation and the existence of a global compact Abelian gauge group is proved. A non-trivial center in the fixed-point net of this gauge group appears, but in an unphysical representation and reducing to the identity in the physical one. The completeness of the described superselection structure, to which the second paper is devoted, is shown in terms of Roberts' net cohomology. Some general features of physical field models defined by twisted cross products of Weyl algebras in non-regular representations are also presented.

arXiv commentpublished final version

References in corpus (16)

• Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
• Modular Structure and Duality in Conformal Quantum Field Theory
• Complementarity of representations in quantum mechanics
• Topological Sectors and a Dichotomy in Conformal Field Theory
• Classification of Two-dimensional Local Conformal Nets with c<1 and 2-cohomology Vanishing for Tensor Categories
• On the representation theory of Virasoro Nets
• Local conformal nets arising from framed vertex operator algebras
• Solitons in Affine and Permutation Orbifolds
• Conformal Orbifold Theories and Braided Crossed G-Categories
• Chiral Observables and Modular Invariants
• Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics
• Superselection Structure of Massive Quantum Field Theories in 1+1 Dimensions
• Two-dimensional models as testing ground for principles and concepts of local quantum physics
• On Soliton Automorphisms in Massive and Conformal Theories
• Quantum massless field in 1+1 dimensions
• Spin-Statistics and CPT for solitons

Cited by in corpus (5)

• Infinite index extensions of local nets and defects
• Topological features of massive bosons on two dimensional Einstein space-time
• Interacting massless infraparticles in 1+1 dimensions
• QED Representation for the Net of Causal Loops
• Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models