1982
DOI: 10.1090/s0002-9947-1982-0637032-8
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Dirac quantum fields on a manifold

Abstract: Abstract. On globally hyperbolic Lorentzian manifolds we construct field operators which satisfy the Dirac equation and have a causal anticommutator. Ambiguities in the construction are removed by formulating the theory in terms of C* algebras of local observables. A generalized form of the Haag-Kastler axioms is verified.Introduction. A Lorentzian manifold is a four dimensional manifold TV/ together with a pseudo-Riemannian metric g of signature ( + , -, -, -). Such manifolds are widely used as models for spa… Show more

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Cited by 116 publications
(170 citation statements)
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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%
“…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%
“…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%
“…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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