### Abstract

The renormalized stress tensor of a free quantum field in a curved space-time should be obtainable by some covariant procedure from the short-distance behavior of the corresponding operator products evaluated at separated points. We perform the covariant expansion of the vacuum expectation value of the point-split stress tensor of a conformally invariant scalar field in a spatially flat Robertson-Walker geometry. When attempting to identify the finite direction-independent part of the coincidence limit of this quantity as the renormalized stress tensor, we encounter ambiguities beyond those corresponding to inevitable renormalizations of coupling constants in the gravitational field equations, but nevertheless limited to local geometrical tensors of fourth order or lower in derivatives of the metric. The ambiguities are resolved by requiring the tensor to be covariantly conserved and to have a trace of the form indicated by recent research on conformal anomalies. Various techniques useful in calculations of this kind are described.

Original language | English (US) |
---|---|

Pages (from-to) | 108-142 |

Number of pages | 35 |

Journal | Annals of Physics |

Volume | 109 |

Issue number | 1 |

DOIs | |

State | Published - 1977 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*109*(1), 108-142. https://doi.org/10.1016/0003-4916(77)90167-1

**Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe.** / Davies, Paul; Fulling, S. A.; Christensen, S. M.; Bunch, T. S.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 109, no. 1, pp. 108-142. https://doi.org/10.1016/0003-4916(77)90167-1

}

TY - JOUR

T1 - Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe

AU - Davies, Paul

AU - Fulling, S. A.

AU - Christensen, S. M.

AU - Bunch, T. S.

PY - 1977

Y1 - 1977

N2 - The renormalized stress tensor of a free quantum field in a curved space-time should be obtainable by some covariant procedure from the short-distance behavior of the corresponding operator products evaluated at separated points. We perform the covariant expansion of the vacuum expectation value of the point-split stress tensor of a conformally invariant scalar field in a spatially flat Robertson-Walker geometry. When attempting to identify the finite direction-independent part of the coincidence limit of this quantity as the renormalized stress tensor, we encounter ambiguities beyond those corresponding to inevitable renormalizations of coupling constants in the gravitational field equations, but nevertheless limited to local geometrical tensors of fourth order or lower in derivatives of the metric. The ambiguities are resolved by requiring the tensor to be covariantly conserved and to have a trace of the form indicated by recent research on conformal anomalies. Various techniques useful in calculations of this kind are described.

AB - The renormalized stress tensor of a free quantum field in a curved space-time should be obtainable by some covariant procedure from the short-distance behavior of the corresponding operator products evaluated at separated points. We perform the covariant expansion of the vacuum expectation value of the point-split stress tensor of a conformally invariant scalar field in a spatially flat Robertson-Walker geometry. When attempting to identify the finite direction-independent part of the coincidence limit of this quantity as the renormalized stress tensor, we encounter ambiguities beyond those corresponding to inevitable renormalizations of coupling constants in the gravitational field equations, but nevertheless limited to local geometrical tensors of fourth order or lower in derivatives of the metric. The ambiguities are resolved by requiring the tensor to be covariantly conserved and to have a trace of the form indicated by recent research on conformal anomalies. Various techniques useful in calculations of this kind are described.

UR - http://www.scopus.com/inward/record.url?scp=0007541565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007541565&partnerID=8YFLogxK

U2 - 10.1016/0003-4916(77)90167-1

DO - 10.1016/0003-4916(77)90167-1

M3 - Article

AN - SCOPUS:0007541565

VL - 109

SP - 108

EP - 142

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 1

ER -