Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept

Bernard Kay

Journées équations aux dérivées partielles (2000)

  • page 1-19
  • ISSN: 0752-0360

Abstract

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Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking effect) and for studying the question whether or not it is possible in principle to manufacture a time-machine. It is a well-established metatheorem that any question concerning such a linear quantum field may be reduced to a definite question concerning the corresponding classical field theory (i.e. linear hyperbolic PDE with non-constant coefficients describing the background in question) - albeit not necessarily a question which would have arisen naturally in a purely classical context. The focus in this talk will be on the covariant Klein-Gordon equation in a fixed curved background, although we shall draw on analogies with other background field problems and with the time-dependent harmonic oscillator. The aim is to give a sketch-impression of the whole subject of Quantum Field Theory in Curved Spacetime, focussing on work with which the author has been personally involved, and also to mention some ideas and work-in-progress by the author and collaborators towards a new “semi-local” vacuum construction for this subject. A further aim is to introduce, and set into context, some recent advances in our understanding of the general structure of quantum fields in curved spacetimes which rely on classical results from microlocal analysis.

How to cite

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Kay, Bernard. "Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept." Journées équations aux dérivées partielles (2000): 1-19. <http://eudml.org/doc/93406>.

@article{Kay2000,
abstract = {Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking effect) and for studying the question whether or not it is possible in principle to manufacture a time-machine. It is a well-established metatheorem that any question concerning such a linear quantum field may be reduced to a definite question concerning the corresponding classical field theory (i.e. linear hyperbolic PDE with non-constant coefficients describing the background in question) - albeit not necessarily a question which would have arisen naturally in a purely classical context. The focus in this talk will be on the covariant Klein-Gordon equation in a fixed curved background, although we shall draw on analogies with other background field problems and with the time-dependent harmonic oscillator. The aim is to give a sketch-impression of the whole subject of Quantum Field Theory in Curved Spacetime, focussing on work with which the author has been personally involved, and also to mention some ideas and work-in-progress by the author and collaborators towards a new “semi-local” vacuum construction for this subject. A further aim is to introduce, and set into context, some recent advances in our understanding of the general structure of quantum fields in curved spacetimes which rely on classical results from microlocal analysis.},
author = {Kay, Bernard},
journal = {Journées équations aux dérivées partielles},
keywords = {Hawking effect; creation of electron positron pairs; black-hole evaporation; covariant Klein-Gordon equation},
language = {eng},
pages = {1-19},
publisher = {Université de Nantes},
title = {Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept},
url = {http://eudml.org/doc/93406},
year = {2000},
}

TY - JOUR
AU - Kay, Bernard
TI - Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
SP - 1
EP - 19
AB - Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking effect) and for studying the question whether or not it is possible in principle to manufacture a time-machine. It is a well-established metatheorem that any question concerning such a linear quantum field may be reduced to a definite question concerning the corresponding classical field theory (i.e. linear hyperbolic PDE with non-constant coefficients describing the background in question) - albeit not necessarily a question which would have arisen naturally in a purely classical context. The focus in this talk will be on the covariant Klein-Gordon equation in a fixed curved background, although we shall draw on analogies with other background field problems and with the time-dependent harmonic oscillator. The aim is to give a sketch-impression of the whole subject of Quantum Field Theory in Curved Spacetime, focussing on work with which the author has been personally involved, and also to mention some ideas and work-in-progress by the author and collaborators towards a new “semi-local” vacuum construction for this subject. A further aim is to introduce, and set into context, some recent advances in our understanding of the general structure of quantum fields in curved spacetimes which rely on classical results from microlocal analysis.
LA - eng
KW - Hawking effect; creation of electron positron pairs; black-hole evaporation; covariant Klein-Gordon equation
UR - http://eudml.org/doc/93406
ER -

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