1,722,389 research outputs found
Entropy of coherent excitations
No full textWe provide a rigorous, explicit formula for the vacuum relative entropy of a coherent state on wedge local von Neumann algebras associated with a free, neutral quantum field theory on the Minkowski spacetime of arbitrary spacetime dimension. We con- sider charges localised on the time-zero hyperplane, possibly crossing the boundary
The emergence of time
No full textClassically, one could imagine a completely static space, thus without time. As is known, this picture is unconceivable in quantum physics due to vacuum fluctuations. The fundamental difference between the two frameworks is that classical physics is commutative (simultaneous observables) while quantum physics is intrinsically noncommutative (Heisenberg uncertainty relations). In this sense, we may say that time is generated by noncommutativity; if this statement is correct, we should be able to derive time out of a noncommutative space.We know that a von Neumann algebra is a noncommutative space. About 50 years ago the Tomita-Takesaki modular theory revealed an intrinsic evolution associated with any given (faithful, normal) state of a von Neumann algebra, so a noncommutative space is intrinsically dynamical. This evolution is characterised by the Kubo-Martin-Schwinger thermal equilibrium condition in quantum statistical mechanics (Haag, Hugenholtz, Winnink), thus modular time is related to temperature. Indeed, positivity of temperature fixes a quantum-thermodynamical arrow of time.We shall sketch some aspects of our recent work extending the modular evolution to a quantum operation (completely positive map) level and how this gives a mathematically rigorous understanding of entropy bounds in physics and information theory. A key point is the relation with Jones' index of subfactors.In the last part, we outline further recent entropy computations in relativistic quantum field theory models by operator algebraic methods, that can be read also within classical information theory. The information contained in a classical wave packet is defined by the modular theory of standard subspaces and related to the quantum null energy inequality. (C) 2020 Elsevier GmbH. All rights reserved
Conformal subnets and intermediate subfactors
No full textGiven an irreducible local conformal net A of von Neumann algebras on S1 and a finite-index conformal subnet B ⊂ A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu for the orbifold construction. By applying previous results of Xu, many coset models turn out to be completely rational and the structure results in [27] hold. Our proofs are based on an analysis of the net inclusion B ⊂ A; among other things we show that, for a fixed interval I, every von Neumann algebra R intermediate between B(I) and A(I) comes from an intermediate conformal net £ between B and A with £(I) = R. We make use of a theorem of Watatani (type II case) and Teruya and Watatani (type III case) on the finiteness of the set script J sign(N, M) of intermediate subfactors in an irreducible inclusion of factors N ⊂ M with finite Jones index [M : N]. We provide a unified proof of this result that gives in particular an explicit bound for the cardinality of script J sign(N, M) which depends only on [M : N]
Index of subfactors and statistics of quantum fields - II. Correspondences, braid group statistics and Jones polynomial
No full textThe endomorphism semigroup End(M) of an infinite factor M is endowed with a natural conjugation (modulo inner automorphisms) {Mathematical expression}, where γ is the canonical endomorphism of M into Ï(M). In Quantum Field Theory conjugate endomorphisms are shown to correspond to conjugate superselection sectors in the description of Doplicher, Haag and Roberts. On the other hand one easily sees that conjugate endomorphisms correspond to conjugate correspondences in the setting of A. Connes. In particular we identify the canonical tower associated with the inclusion[Figure not available: see fulltext.] relative to a sector Ï. As a corollary, making use of our previously established index-statistics correspondence, we completely describe, in low dimensional theories, the statistics of a selfconjugate superselection sector Ï with 3 or less channels, in particular of sectors with statistical dimension d(Ï)<2, by obtaining the braid group representations of V. Jones and Birman, Wenzl and Murakami. The statistics is thus described in these cases by the polynomial invariants for knots and links of Jones and Kauffman. Selconjugate sectors are subdivided into real and pseudoreal ones and the effect of this distinction on the statistics is analyzed. The FYHLMO polynomial describes arbitrary 2-channels sectors. © 1990 Springer-Verlag
A simple proof of the existence of the modular automorphisms in approximately finite dimensional von Neumann algebras
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