Casimir Effect and Global Theory of Boundary Conditions

Details Casimir Effect and Global Theory of Boundary Conditions Casimir Effect and Global Theory of Boundary Conditions

2006-04-12

arxiv.org/abs/hep-th/0604089v1

J.Phys.A39:6127-6136,2006

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1088/0305-4470/39/21/S03

The consistency of quantum field theories defined on domains with external borders imposes very restrictive constraints on the type of boundary conditions that the fields can satisfy. We analyse the global geometrical and topological properties of the space of all possible boundary conditions for scalar quantum field theories. The variation of the Casimir energy under the change of boundary conditions reveals the existence of singularities generically associated to boundary conditions which either involve topology changes of the underlying physical space or edge states with unbounded below classical energy. The effect can be understood in terms of a new type of Maslov index associated to the non-trivial topology of the space of boundary conditions. We also analyze the global aspects of the renormalization group flow, T-duality and the conformal invariance of the corresponding fixed points.

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