Buchholz, Detlev

[["dc.bibliographiccitation.firstpage","625"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Communications in Mathematical Physics"],["dc.bibliographiccitation.lastpage","641"],["dc.bibliographiccitation.volume","246"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T10:49:48Z"],["dc.date.available","2018-11-07T10:49:48Z"],["dc.date.issued","2004"],["dc.description.abstract","Employing 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."],["dc.identifier.doi","10.1007/s00220-004-1060-4"],["dc.identifier.isi","000220722400010"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/48514"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","0010-3616"],["dc.title","An algebraic characterization of vacuum states in Minkowski space. III. Reflection maps"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","475"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Reviews in Mathematical Physics"],["dc.bibliographiccitation.lastpage","560"],["dc.bibliographiccitation.volume","12"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Dreyer, O."],["dc.contributor.author","Florig, M."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T08:31:49Z"],["dc.date.available","2018-11-07T08:31:49Z"],["dc.date.issued","2000"],["dc.description.abstract","A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete spacetimes - four-dimensional Minkowski and three-dimensional de Sitter spaces - for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated."],["dc.identifier.doi","10.1142/S0129055X00000174"],["dc.identifier.isi","000087964300001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/17202"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","World Scientific Publ Co Pte Ltd"],["dc.relation.issn","0129-055X"],["dc.title","Geometric modular action and spacetime symmetry groups"],["dc.type","review"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2147"],["dc.bibliographiccitation.issue","9"],["dc.bibliographiccitation.journal","Journal of Physics A Mathematical and Theoretical"],["dc.bibliographiccitation.lastpage","2163"],["dc.bibliographiccitation.volume","40"],["dc.contributor.author","Buchholz, Detlev"],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T11:04:10Z"],["dc.date.available","2018-11-07T11:04:10Z"],["dc.date.issued","2007"],["dc.description.abstract","We 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."],["dc.identifier.doi","10.1088/1751-8113/40/9/019"],["dc.identifier.isi","000245026500021"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/51773"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","1751-8113"],["dc.title","String- and brane-localized causal fields in a strongly nonlocal model"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","L31"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Classical and Quantum Gravity"],["dc.bibliographiccitation.lastpage","L37"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Florig, M."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T10:57:34Z"],["dc.date.available","2018-11-07T10:57:34Z"],["dc.date.issued","2000"],["dc.description.abstract","If 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."],["dc.identifier.doi","10.1088/0264-9381/17/2/102"],["dc.identifier.isi","000085159100002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/50286"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","0264-9381"],["dc.title","The second law of thermodynamics, TCP and Einstein causality in anti-de Sitter spacetime"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.subtype","letter_note"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","17"],["dc.bibliographiccitation.issue","1-2"],["dc.bibliographiccitation.journal","Physics Letters A"],["dc.bibliographiccitation.lastpage","21"],["dc.bibliographiccitation.volume","337"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T11:15:15Z"],["dc.date.available","2018-11-07T11:15:15Z"],["dc.date.issued","2005"],["dc.description.abstract","It 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."],["dc.identifier.doi","10.1016/j.physleta.2005.01.055"],["dc.identifier.isi","000227654000003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/54326"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Elsevier Science Bv"],["dc.relation.issn","0375-9601"],["dc.title","Quantum statistics and locality"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","PII S0264-9381(02)39442-5"],["dc.bibliographiccitation.firstpage","6417"],["dc.bibliographiccitation.issue","24"],["dc.bibliographiccitation.journal","Classical and Quantum Gravity"],["dc.bibliographiccitation.lastpage","6434"],["dc.bibliographiccitation.volume","19"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Mund, J."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T09:41:37Z"],["dc.date.available","2018-11-07T09:41:37Z"],["dc.date.issued","2002"],["dc.description.abstract","We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker spacetimes. We show that the worldline of an observer in such spacetimes determines a unique orbit in the identity component SO0(4,1) of the local conformal group of the spacetime and that this orbit determines a unique transport on the spacetime. For a quantum system on the spacetime modelled 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 'quasicovariant' 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."],["dc.identifier.doi","10.1088/0264-9381/19/24/310"],["dc.identifier.isi","000180414100011"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33773"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","0264-9381"],["dc.title","Covariant and quasi-covariant quantum dynamics in Robertson-Walker spacetimes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","607"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Annales Henri Poincaré"],["dc.bibliographiccitation.lastpage","624"],["dc.bibliographiccitation.volume","6"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T10:56:54Z"],["dc.date.available","2018-11-07T10:56:54Z"],["dc.date.issued","2005"],["dc.description.abstract","We 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."],["dc.identifier.doi","10.1007/s00023-005-0217-9"],["dc.identifier.isi","000231650100001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/50123"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Birkhauser Verlag Ag"],["dc.relation.issn","1424-0637"],["dc.title","Geometric modular action and spontaneous symmetry breaking"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","4810"],["dc.bibliographiccitation.issue","12"],["dc.bibliographiccitation.journal","Journal of Mathematical Physics"],["dc.bibliographiccitation.lastpage","4831"],["dc.bibliographiccitation.volume","45"],["dc.contributor.author","Buchholz, D."],["dc.contributor.author","Summers, Stephen J."],["dc.date.accessioned","2018-11-07T10:43:30Z"],["dc.date.available","2018-11-07T10:43:30Z"],["dc.date.issued","2004"],["dc.description.abstract","If 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."],["dc.identifier.doi","10.1063/1.1804230"],["dc.identifier.isi","000226697100025"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/47066"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Inst Physics"],["dc.relation.issn","0022-2488"],["dc.title","Stable quantum systems in anti-de Sitter space: Causality, independence, and spectral properties"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]