scholarly journals An Indefinite Metric Model for Interacting Quantum Fields on Globally Hyperbolic Space-Times

2003 ◽  
Vol 4 (4) ◽  
pp. 637-659
Author(s):  
Hanno Gottschalk ◽  
Horst Thaler
Keyword(s):  
Hyperbolic Space ◽  
Indefinite Metric ◽  
Quantum Fields ◽  
Globally Hyperbolic ◽  
Metric Model

scholarly journals Scattering Theory for Quantum Fields¶with Indefinite Metric

2001 ◽  
Vol 216 (3) ◽  
pp. 491-513 ◽  
Author(s):  
Sergio Albeverio ◽  
Hanno Gottschalk
Keyword(s):  
Scattering Theory ◽  
Indefinite Metric ◽  
Quantum Fields

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.

Orthomodular lattice in Lorentzian globally hyperbolic space-time

2017 ◽  
Vol 79 (2) ◽  
pp. 187-195 ◽  
Author(s):  
Wojciech Cegła ◽  
Bernard Jancewicz ◽  
Jan Florek
Keyword(s):  
Hyperbolic Space ◽  
Orthomodular Lattice ◽  
Space Time ◽  
Globally Hyperbolic

Black hole physics in globally hyperbolic space-times

Pramana ◽  
1982 ◽  
Vol 18 (5) ◽  
pp. 385-396 ◽  
Author(s):  
P S Joshi ◽  
J V Narlikar
Keyword(s):  
Black Hole ◽  
Hyperbolic Space ◽  
Black Hole Physics ◽  
Globally Hyperbolic

scholarly journals Cauchy problem on non-globally hyperbolic space-times

2008 ◽  
Vol 157 (3) ◽  
pp. 1646-1654 ◽  
Author(s):  
I. Ya. Aref’eva ◽  
T. Ishiwatari ◽  
I. V. Volovich
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Space ◽  
Globally Hyperbolic

scholarly journals Models of Local Relativistic Quantum Fields with Indefinite Metric (in All Dimensions)

1997 ◽  
Vol 184 (3) ◽  
pp. 509-531 ◽  
Author(s):  
S. Albeverio ◽  
H. Gottschalk ◽  
J.-L.- Wu
Keyword(s):  
Relativistic Quantum ◽  
Indefinite Metric ◽  
Quantum Fields

Cauchy surfaces in a globally hyperbolic space‐time

1988 ◽  
Vol 29 (3) ◽  
pp. 578-579 ◽  
Author(s):  
Jan Dieckmann
Keyword(s):  
Hyperbolic Space ◽  
Space Time ◽  
Globally Hyperbolic

scholarly journals MICROLOCAL SPECTRUM CONDITION AND HADAMARD FORM FOR VECTOR-VALUED QUANTUM FIELDS IN CURVED SPACETIME

2001 ◽  
Vol 13 (10) ◽  
pp. 1203-1246 ◽  
Author(s):  
HANNO SAHLMANN ◽  
RAINER VERCH
Keyword(s):  
Vector Bundle ◽  
Scalar Fields ◽  
Quantum Fields ◽  
Curved Spacetime ◽  
Globally Hyperbolic ◽  
Commutation Relations ◽  
Hyperbolic Spacetime ◽  
Hadamard Condition ◽  
Spectrum Condition ◽  
Hadamard States

Some years ago, Radzikowski has found a characterization of Hadamard states for scalar quantum fields on a four-dimensional globally hyperbolic spacetime in terms of a specific form of the wavefront set of their two-point functions (termed "wavefront set spectrum condition"), thereby initiating a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, we extend this important result on the equivalence of the wavefront set spectrum condition with the Hadamard condition from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance saling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.

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