Dirac quantum fields on a manifold

Dimock, J.

doi:10.1090/s0002-9947-1982-0637032-8

Cited by 115 publications

(170 citation statements)

References 21 publications

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“…One could work with Dirac spinors as well; then one has to introduce appropriate 'doublings' of spinor bundle and Dirac operator. Such an approach has, in the context of quantizing Dirac fields, been favoured elsewhere [11,21,27,29,35]. By employing somewhat more elaborate notation, one may generalize our results in Chapter 5 to the slightly more general case of Dirac spinors.…”

Section: Spin Structures and Spinor Fieldsmentioning

confidence: 91%

Microlocal Spectrum Condition and Hadamard Form for Vector-Valued Quantum Fields in Curved Spacetime

2001

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Abstract.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 scaling 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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Section: Spin Structures and Spinor Fieldsmentioning

confidence: 91%

Microlocal Spectrum Condition and Hadamard Form for Vector-Valued Quantum Fields in Curved Spacetime

2001

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“…21 For obviously local primitive causality entails entails (QNSP1) for any S. It has been veri…ed that local primitive causality holds for the quantized Klein-Gordon …eld and the Dirac …eld (see Dimock 1980Dimock , 1982. The upshot is that if (QNSP1) does adequately capture no superluminal propagation for quantum …elds, local primitive causality is su¢ cient to ensure no superluminal propagation even at very small scales despite the failure of various energy conditions at these scales.…”

Section: Causal Propagation For Quantum …Eldsmentioning

confidence: 99%

No superluminal propagation for classical relativistic and relativistic quantum fields

Earman

2014

Studies in History and Philosophy of Science Part B: Studies in

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A criterion is proposed to ensure that classical relativistic …elds do not propagate superluminally. If this criterion does indeed serve as a su¢ cient condition for no superluminal propagation it follows that various other criteria found in the physics literature cannot serve as necessary conditions since they can fail although the pro¤ered condition holds. The rejected criteria rely on energy conditions that are believed to hold for most classical …elds used in actual applications. But these energy conditions are known to fail at small scales for quantum …elds. It is argued that such a failure is not necessarily a cause for concern about superluminal propagation in the quantum regime since the pro¤ered criterion of no superluminal propagation for classical …elds has a natural analog for quantum …elds and, further, this quantum analog condition provably holds for some quantum …elds despite the violation of energy conditions. The apparatus developed here also o¤ers a di¤erent approach to treating the Reichenbach-Salmon cases of "pseudo-causal processes" and helps to clarify the issue of whether relativity theory is consistent with superluminal propagation.

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“…We adopt the approach of Dirac quantum fields in the spirit of [16] and [17]. This approach is explained in Section 5.2.…”

Section: Chapter 5 Dirac Quantum Fieldsmentioning

confidence: 99%

“…Then 17) are respectively selfadjoint on h + and h − , and the classical fields of one particle, φ + , and of one antiparticle, φ − , are solutions to a Schrödinger type equation on h +(−) :…”

Section: Second Quantization Of Dirac Fieldsmentioning

confidence: 99%

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Creation of fermions by rotating charged black holes

Häfner¹

2009

Mémoires Soc. Math. France

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:This work is devoted to the mathematical study of the Hawking effect for fermions in the setting of the collapse of a rotating charged star. We show that an observer who is located far away from the star and at rest with respect to the Boyer Lindquist coordinates observes the emergence of a thermal state when his proper time goes to infinity. We first introduce a model of the collapse of the star. We suppose that the space-time outside the star is given by the Kerr-Newman metric. The assumptions on the asymptotic behavior of the surface of the star are inspired by the asymptotic behavior of certain timelike geodesics in the Kerr-Newman metric. The Dirac equation is then written using coordinates and a Newman-Penrose tetrad which are adapted to the collapse. This coordinate system and tetrad are based on the so called simple null geodesics. The quantization of Dirac fields in a globally hyperbolic space-time is described. We formulate and prove a theorem about the Hawking effect in this setting. The proof of the theorem contains a minimal velocity estimate for Dirac fields that is slightly stronger than the usual ones and an existence and uniqueness result for solutions of a characteristic Cauchy problem for Dirac fields in the Kerr-Newman space-time. In an appendix we construct explicitly a Penrose compactification of block I of the Kerr-Newman space-time based on simple null geodesics. Résumé :Ce travail est dédiéà l'étude mathématique de l'effet Hawking pour des fermions dans le cadre de l'effondrement d'uneétoile chargée en rotation. On démontre qu'un observateur localisé loin de l'étoile et au repos par rapport aux coordonnées de BoyerLindquist observe l'émergence d'unétat thermal quand son temps propre tend vers l'infini. On introduit d'abord un modèle de l'effondrement de l'étoile. On suppose que l'espace-tempsà l'extérieur de l'étoile est donné par la métrique de Kerr-Newman. Les hypothèses sur le comportement asymptotique de la surface de l'étoile sont inspirées par le comportement asymptotique de certaines géodésiques de type temps dans la métrique de Kerr-Newman. L'équation de Dirac est alorsécrite en utilisant des coordonnées et une tétrade de Newman-Penrose adaptésà l'effondrement. Ce système de coordonnées et cette tétrade sont basés sur des géodésiques qu'on appelle des géodésiques simples isotropes. La quantification des champs de Dirac dans un espace-temps globalement hyperbolique est décrite. On formule un théorème sur l'effet Hawking dans ce cadre. La preuve du théorème contient une estimation de vitesse minimale pour les champs de Dirac légèrement plus forte que les estimations usuelles ainsi qu'un résultat d'existence et d'unicité pour les solutions d'un problème caractéristique pour les champs de Dirac dans l'espace-temps de Kerr-Newman. Dans un appendice, nous construisons explicitement la compactification de Penrose du bloc I de l'espace-temps de Kerr-Newman qui est basée sur les géodésiques simples isotropes.2000 Mathematics Subject Classification : 35P25, 35Q75, 58J45, 83C47, 8...

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Dirac quantum fields on a manifold

Cited by 115 publications

References 21 publications

Microlocal Spectrum Condition and Hadamard Form for Vector-Valued Quantum Fields in Curved Spacetime

Microlocal Spectrum Condition and Hadamard Form for Vector-Valued Quantum Fields in Curved Spacetime

No superluminal propagation for classical relativistic and relativistic quantum fields

Creation of fermions by rotating charged black holes

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