2,331 research outputs found
Stable quantum systems in anti–de Sitter space: Causality, independence, and spectral properties
No full textIf a state is passive for uniformly accelerated observers in n-dimensional (ngreater than or equal to2) anti-de Sitter (Ads) space-time (i.e., cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a "geodesic causal structure" on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded space-time regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space-time localization. Examples are provided of models satisfying the hypotheses of these theorems. (C) 2004 American Institute of Physics
An algebraic characterization of vacuum states in Minkowski space. III. Reflection maps
No full textEmploying the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding state a continuous unitary representation of the proper Poincare group which acts covariantly on the net and leaves the state invariant. The present results and methods substantially improve upon previous work. In particular, the continuity properties of the representation are shown to be a consequence of the net structure, and surmised cohomological problems in the construction of the representation are resolved by demonstrating that, for the Poincare group, continuous reflection maps are restrictions of continuous homomorphisms
String- and brane-localized causal fields in a strongly nonlocal model
No full textWe study a weakly local, but nonlocal model in spacetime dimension d >= 2 and prove that it is maximally nonlocal in a certain specific quantitative sense. Nevertheless, depending on the number of dimensions d, it has string-localized or brane-localized operators which commute at spatial distances. In two spacetime dimensions, the model even comprises a covariant and local subnet of operators localized in bounded subsets of Minkowski space which has a nontrivial scattering matrix. The model thus exemplifies the algebraic construction of local operators from algebras associated with nonlocal fields
Quantum statistics and locality
No full textIt is shown that two observers have mutually commuting observables if they are able to prepare in each subsector of their common state space some state exhibiting no mutual correlations. This result establishes a heretofore missing link between statistical and locality (commensurability) properties of observables in relativistic quantum physics. The analysis is based on a discussion of coincidence experiments and leads to a quantitative measure of deviation from locality. Hence, it may be applied in intrinsically nonlocal theories such as string theory and field theory on noncommutative spacetime. (c) 2005 Elsevier B.V. All rights reserved
Geometric modular action and spontaneous symmetry breaking
No full textWe study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space-times. We show that any internal symmetry group must commute with the representation of the Poincare group (whose existence is assured by the CGMA) and each translation-invariant vector is also Poincare invariant. The subspace of these vectors can be centrally decomposed into pure invariant states and the CGMA holds in the resulting sectors. As positivity of the energy is not assumed, similar results may be expected to hold for other space-times
Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times
No full textWe propose a canonical description of the dynamics of quantum systems on a
class of Robertson-Walker space-times. We show that the worldline of an
observer in such space-times determines a unique orbit in the local conformal
group SO(4,1) of the space-time and that this orbit determines a unique
transport on the space-time. For a quantum system on the space-time modeled by
a net of local algebras, the associated dynamics is expressed via a suitable
family of ``propagators''. In the best of situations, this dynamics is
covariant, but more typically the dynamics will be ``quasi-covariant'' in a
sense we make precise. We then show by using our technique of ``transplanting''
states and nets of local algebras from de Sitter space to Robertson-Walker
space that there exist quantum systems on Robertson-Walker spaces with
quasi-covariant dynamics. The transplanted state is locally passive, in an
appropriate sense, with respect to this dynamics.Comment: 21 pages, 1 figur
The second law of thermodynamics, TCP and Einstein causality in anti-de Sitter spacetime
No full textIf the vacuum is passive for uniformly accelerated observers in anti-de Sitter spacetime (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Hawking-Unruh temperature, (b) discover a TCP symmetry and (c) find that observables in complementary wedge-shaped regions are commensurable (local) in the vacuum state. These results are model independent and hold in any theory which is compatible with some weak notion of spacetime localization
Bedrock Geologic Map of the Brule River area, Pine Mountain Quadrangle, Cook County, Minnesota, USA
No full textFix, Paul J; Ginley, Stephen J; Schraeder, Lauren A; Summers, Aaron J; Boerboom, Terrence J; Doyle, Mike M. (2013). Bedrock Geologic Map of the Brule River area, Pine Mountain Quadrangle, Cook County, Minnesota, USA. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/257392
Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
No full textWarped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical systems with automorphic actions of R^n, whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita-Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations
Further Representations of the Canonical Commutation Relations
No full text. We construct a new class of representations of the canonical commutation relations, which generalizes previously known classes. We perturb the infinitesimal generator of the initial Fock representation (i.e. the free quantum field) by a function of the field which is square-integrable with respect to the associated Gaussian measure. We characterize which such perturbations lead to representations of the canonical commutation relations. We provide conditions entailing the irreducibility of such representations, show explicitly that our class of representations subsumes previously studied classes, and give necessary and sufficient conditions for our representations to be unitarily equivalent, resp. quasi-equivalent, with Fock, coherent or quasifree representations. Typeset by A M S-T E X 2 MARTIN FLORIG AND STEPHEN J. SUMMERS I. Introduction The canonical commutation relations (henceforth the CCR) were initially introduced in 1927 by Dirac as generalizations of Heisenberg's commuta..
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