C. D. Fosco

The proximity force approximation for the Casimir energy as a derivative expansion

The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next to leading order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function

Casimir energies with finite-width mirrors

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Vortices and bags in (2+1)-dimension

in front of a plane. By regarding the Casimir energy as a functional of

Casimir effect with dynamical matter on thin mirrors

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Derivative-expansion approach to the interaction between close surfaces

, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of corresponding NTLO correction, which involves two derivatives of

Vacuum fluctuations and generalized boundary conditions

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Derivative expansion for the boundary interaction terms in the Casimir effect: Generalized δ potentials

. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy.

Anomalies and symmetries of the regularized action

We use a functional approach to the Casimir effect in order to evaluate the exact vacuum energy for a real scalar field in d+1 dimensions, in the presence of backgrounds that, in a particular limit, impose Dirichlet boundary conditions on one or two parallel surfaces. Outside of that limit, the backgrounds are described by a nonlocal effective action and may be thought of as modelling finite-width mirrors with frequency-dependent transmission and reflection coefficients. We obtain formal expressions for the Casimir energy in general backgrounds, and provide new explicit results in some particular cases.

Neumann Casimir effect: A singular boundary-interaction approach

We consider the effect of the (heavy) fundamental quarks on the low energy effective Lagrangian description of nonabelian gauge theories in 2+1 dimensions. We show that in the presence of the fundamental charges, the magnetic

Casimir free energy at high temperatures: Grounded versus isolated conductors

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