scholarly journals Remarks on the modular operator and local observables

1978 ◽  
Vol 61 (3) ◽  
pp. 267-273 ◽  
Author(s):  
Carlo Rigotti
Keyword(s):  
Local Observables ◽  
Modular Operator

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Non-local observables and lightcone-averaging in relativistic thermodynamics

2009 ◽  
Vol 5 (10) ◽  
pp. 741-747 ◽  
Author(s):  
Jörn Dunkel ◽  
Peter Hänggi ◽  
Stefan Hilbert
Keyword(s):  
Non Local ◽  
Local Observables ◽  
Relativistic Thermodynamics

scholarly journals Two local observables are sufficient to characterize maximally entangled states ofNqubits

2011 ◽  
Vol 83 (2) ◽  
Author(s):  
Fengli Yan ◽  
Ting Gao ◽  
Eric Chitambar
Keyword(s):  
Entangled States ◽  
Maximally Entangled States ◽  
Local Observables

SYMMETRIES IN THEORY OF LOCAL OBSERVABLES AND THE CHOICE OF THE NET OF LOCAL ALGEBRAS

1992 ◽  
Vol 04 (spec01) ◽  
pp. 1-14 ◽  
Author(s):  
HUZIHIRO ARAKI
Keyword(s):  
Scattering Theory ◽  
Local Observable ◽  
Particle Spectrum ◽  
Massive Scalar ◽  
Local Algebras ◽  
Local Observables ◽  
Physical Consequences ◽  
Sector Theory ◽  
Internal Symmetries

For a given net of algebras of local observables, satisfying standard assumptions, we propose the problem of classifying a net of subalgebras which provides the same physical consequences (possibly via Doplicher-Haag-Roberts sector theory) such as particle spectrum and scattering theory. The notion of symmetry of the net of local algebras are introduced and its geometrical aspects are analyzed, with the conclusion that the net reproduces the geometry of supporting regions to some extent. The internal symmetries provides a possible net of subalgebras, as is discussed by Doplicher, Haag and Roberts. We discuss other possibilities by generating subalgebras from a local observable. Results and problems for the simple case of a neutral massive scalar free Held are summarized.

scholarly journals Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

2019 ◽  
Vol 20 (12) ◽  
pp. 3889-3926
Author(s):  
Henning Bostelmann ◽  
Daniela Cadamuro
Keyword(s):  
Bound States ◽  
Von Neumann Algebras ◽  
Form Factors ◽  
Explicit Construction ◽  
Local Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Von Neumann ◽  
Local Observables ◽  
Wightman Axioms

Abstract We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh–Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model.

scholarly journals HOMOTOPY OF POSETS, NET-COHOMOLOGY AND SUPERSELECTION SECTORS IN GLOBALLY HYPERBOLIC SPACE-TIMES

2005 ◽  
Vol 17 (09) ◽  
pp. 1021-1070 ◽  
Author(s):  
GIUSEPPE RUZZI
Keyword(s):  
Hyperbolic Space ◽  
Space Time ◽  
Fundamental Groups ◽  
Mathematical Framework ◽  
Permutation Symmetry ◽  
Index Set ◽  
Globally Hyperbolic ◽  
Underlying Space ◽  
Local Observables ◽  
Suitable Change

We study sharply localized sectors, known as sectors of DHR-type, of a net of local observables, in arbitrary globally hyperbolic space-times with dimension ≥ 3. We show that these sectors define, as it happens in Minkowski space, a C*-category in which the charge structure manifests itself by the existence of a tensor product, a permutation symmetry and a conjugation. The mathematical framework is that of the net-cohomology of posets according to J. E. Roberts. The net of local observables is indexed by a poset formed by a basis for the topology of the space-time ordered under inclusion. The category of sectors, is equivalent to the category of 1-cocycles of the poset with values in the net. We succeed in analyzing the structure of this category because we show how topological properties of the space-time are encoded in the poset used as index set: the first homotopy group of a poset is introduced and it is shown that the fundamental group of the poset and one of the underlying space-time are isomorphic; any 1-cocycle defines a unitary representation of these fundamental groups. Another important result is the invariance of the net-cohomology under a suitable change of index set of the net.

scholarly journals Thermalization of local observables in small Hubbard lattices

2012 ◽  
Vol 86 (2) ◽  
Author(s):  
S. Genway ◽  
A. F. Ho ◽  
D. K. K. Lee
Keyword(s):  
Local Observables

The Wave Function and Local Observables in the STA

2016 ◽  
pp. 527-530
Author(s):  
Anatoli Babin ◽  
Alexander Figotin
Keyword(s):  
Wave Function ◽  
Local Observables
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