Scalar Field Theory in Curved Space and the Definition of Momentum

dc.creatorDavis, Simon
dc.date1997-02-09
dc.date1997-12-22
dc.date.accessioned2026-07-07T09:04:35Z
dc.date.available2026-07-07T09:04:35Z
dc.descriptionSome general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of constant curvature which could arise in the local description of matter interactions in small regions of space-time. Transform space rules for evaluating Feynman diagrams in Euclidean anti-de Sitter space are initially defined using eigenfunctions based on generalized plane waves. It is shown that, for a general curved space, the rules associated with the vertex are dependent on the type of interaction being considered. A condition for eliminating this dependence is given. It is demonstrated that the vacuum and propagator in conformally flat coordinates in anti-de Sitter space are equivalent to those analytically continued from $H^4$ and that transform space rules based on these coordinates can be used more readily. A proof of the analogue of Goldstone's theorem in anti-de Sitter space is given, using a generalized plane wave representation of the commutator of the current and the scalar field. It is shown that the introduction of curvature in the space-time shifts the momentum by an amount which is determined by the Riemann tensor to first order, and it follows that there is a shift in both the momentum and mass scale in anti-de Sitter space.
dc.description44 pages, TeX, 3 figures. Minor alterations have been made to several equations in the text
dc.identifierhttps://arxiv.org/abs/hep-th/9702070
dc.identifierhttp://arxiv.org/abs/hep-th/9702070
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149432
dc.subjectHigh Energy Physics - Theory
dc.titleScalar Field Theory in Curved Space and the Definition of Momentum
dc.typetext

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