# Advances in the Casimir Effect (International Series of by Michael Bordag, Galina Leonidovna Klimchitskaya, Umar

By Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, Vladimir Mikhaylovich Mostepanenko

The topic of this publication is the Casimir impact, a manifestation of zero-point oscillations of the quantum vacuum leading to forces appearing among heavily spaced our bodies. For the advantage of the reader, the ebook assembles field-theoretical foundations of this phenomenon, functions of the overall conception to genuine fabrics, and a entire description of all lately played measurements of the Casimir strength with a comparability among scan and concept. there's an pressing desire for a ebook of this kind, given the rise of curiosity in forces originating from the quantum vacuum. a variety of new effects were bought within the previous couple of years which aren't mirrored in past books at the topic, yet that are very promising for basic technological know-how and nanotechnology. The ebook is a distinct resource of data featuring a severe overview of the entire major effects and methods from 1000s of magazine papers. It additionally outlines new principles that have now not but been universally permitted yet that are discovering expanding aid from test.

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The application region of the pairwise summation method for rough and corrugated surfaces is determined by the more fundamental path integral approach (which is valid for ideal metal boundaries) and by the statistical approach, taking the roughness correlation length and the nonideality of the metal into account. The role of surface roughness in the atom-wall interaction is discussed at the end of the chapter. The most striking developments in the Casimir eﬀect during the last ten years are new, more precise measurements of the Casimir force using modern technology.

38), does not contain a contribution linear in the mass. The physical explanation for this fact is that the space with the topology of a circle does not 26 Simple models of the Casimir eﬀect contain boundary points and hence the vacuum energy does not contain their energy. 47) leads to (Mamayev and Trunov 1979a) c ∞ y dy π c E(a, 0) = E(a) = − =− . e. the Casimir energy is exponentially small. At the end of this section, we brieﬂy discuss what are referred to as antiperiodic conditions imposed on a scalar ﬁeld, ϕ(t, x + a) = −ϕ(t, x).

Now we consider the total vacuum energy of the scalar ﬁeld in the quantization volume V . 42) on the boundary surface S. 51), the following result is obtained: 1 (0) E0 = dr 0|T00 (x)|0 = ωJ . 59) has been integrated by parts. 1. 59): (0) 0M |T00 (x)|0M = dk ωk . 61) The total vacuum energy in the volume V is (0) dr 0M |T00 (x)|0M = E0 = V 1 2 dk ωk V. 66), obtained in two-dimensional space–time. 2). We consider now the quantization of an electromagnetic ﬁeld in the presence of boundaries. This is a nontrivial problem, owing to the existence of diﬀerent polarization states of the photon.