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Operator algebra

About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.


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Journal ArticleDOI
TL;DR: In this paper, a reduced theory which is invariant with respect to the new chiral algebra was constructed, which is generated by the stress-energy tensor, two bosonic currents with spins 3/2 and the U(1) current.
Abstract: Constraining theSL(3) WZW-model we construct a reduced theory which is invariant with respect to the new chiral algebraW 3 2 . This symmetry is generated by the stress-energy tensor, two bosonic currents with spins 3/2 and theU(1) current. We conjecture a Kac formula that describes the highly reducible representation for this algebra. We also discuss the quantum Hamiltonian reduction for the general type of constraints that leads to the new extended conformal algebras.

208 citations

Journal ArticleDOI
TL;DR: In this article, the Weyl correspondence between classical and quantum observables is rigorously formulated for a linear mechanical system with a finite number of degrees of freedom, where a multiplication of functions and a *-operation are introduced to make the Hilbert space of Lebesgue square-integrable complex-valued functions on phase space into a H*-algebra.
Abstract: The Weyl correspondence between classical and quantum observables is rigorously formulated for a linear mechanical system with a finite number of degrees of freedom. A multiplication of functions and a *‐operation are introduced to make the Hilbert space of Lebesgue square‐integrable complex‐valued functions on phase space into a H*‐algebra. The Weyl correspondence is realized as a *‐isomorphism f → W(f) of this H*‐algebra onto the H*‐algebra of Hilbert‐Schmidt operators on the Hilbert space of Lebesgue square‐integrable complex‐valued functions on configuration space. Moreover, the kernel of W(f) is exhibited in terms of a Fourier‐Plancherel transform of f. Elementary properties of the Wigner quasiprobability density function and its characteristic function are deduced and used to obtain these results.

208 citations

Journal ArticleDOI
TL;DR: In this article, a class of 2D statistical mechanics models known as IRF models can be viewed as a subalgebra of the operator algebra of vertex models, and an explicit intertwiner between two representations of this sub-algebra is obtained.
Abstract: We show that a class of 2D statistical mechanics models known as IRF models can be viewed as a subalgebra of the operator algebra of vertex models. Extending the Wigner calculus to quantum groups, we obtain an explicit intertwiner between two representations of this subalgebra.

208 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare group on the one-particle Hilbert space.
Abstract: We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano–Wichmann relations and a representation of the Poincare group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita–Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh–Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and of de Sitter spacetime.

207 citations

Book ChapterDOI
01 Feb 2006
TL;DR: Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools as mentioned in this paper.
Abstract: Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.

206 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202337
202277
2021125
2020141
2019173
2018169