O(N)quantum fields in curved spacetime

After a review of conformal symmetry, this chapter covers the quantisation of fields in curved space-times. It is shown that field operators defined with respect to different vacua are related by a Bogolyubov transformation and that the mixing of positive and negative frequencies determines the amount of particle production. The Unruh effect is explained and it is shown that in a space-time with an event horizon, a thermal spectrum of particles is created close to the horizon.

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Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalizedζfunctions

Physical Review D ◽

10.1103/physrevd.55.6123 ◽

1997 ◽

Vol 55 (10) ◽

pp. 6123-6134 ◽

Cited By ~ 40

Author(s):

Nicholas G. Phillips ◽

B. L. Hu

Keyword(s):

Energy Density ◽

Vacuum Energy ◽

Vacuum Energy Density ◽

Quantum Fields ◽

Curved Spacetime

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Quantum fields in curved spacetime

Physics Reports ◽

10.1016/j.physrep.2015.02.001 ◽

2015 ◽

Vol 574 ◽

pp. 1-35 ◽

Cited By ~ 58

Author(s):

Stefan Hollands ◽

Robert M. Wald

Keyword(s):

Quantum Fields ◽

Curved Spacetime

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

Reviews in Mathematical Physics ◽

10.1142/s0129055x01001010 ◽

2001 ◽

Vol 13 (10) ◽

pp. 1203-1246 ◽

Cited By ~ 61

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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