Quantum field theory on manifolds with a boundary

Abstract

We discuss quantum theory of fields ϕdefined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(ϕ) which is a bilinear form in ϕdefines the Gaussian measure with a covariance (Green function) {\cal G}. We discuss a relation between the quantum field theory with a fixed boundary condition Φand the theory defined by the Green function {\cal G}. It is shown that the latter results by an average over Φof the first. The QFT in (anti)de Sitter space is treated as an example. It is shown that quantum fields on the boundary are more regular than the ones on (anti) de Sitter space.

arXiv commentThe version to appear in Journal of Physics A, a discussion on the relation to other works in the field is added

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Cited by in corpus (2)

• AdS/CFT correspondence in the Euclidean context
• A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction