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

The topic of this booklet 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 booklet assembles field-theoretical foundations of this phenomenon, functions of the final thought to actual fabrics, and a complete description of all lately played measurements of the Casimir strength with a comparability among test and idea. there's an pressing desire for a booklet of this sort, given the rise of curiosity in forces originating from the quantum vacuum. various new effects were received within the previous few years which aren't mirrored in past books at the topic, yet that are very promising for primary technological know-how and nanotechnology. The e-book is a different resource of data providing a severe overview of the entire major effects and ways from hundreds and hundreds of magazine papers. It additionally outlines new rules that have now not but been universally approved yet that are discovering expanding help from test.

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**Extra info for Advances in the Casimir Effect (International Series of Monographs on Physics)**

**Example text**

42) are called the Neumann boundary problem. 43) S where u is some parameter or a function of the radius vector, is called a Robin boundary condition. 1) with m = 0. e. 39), −∇2 AJ,µ (r) = ΛJ AJ,µ (r), ΛJ ≡ ωJ2 . 71) must be satisﬁed at each point of S. 17). For electromagnetic ﬁelds without sources, it is always possible to ﬁx the vector potential such that A0J (r) = 0, divAJ (r) = 0. 47) This is usually referred to as the Coulomb gauge. 48) where the index “t” marks the components of E and AJ tangential to the surface.

60): 28 Simple models of the Casimir eﬀect ∞ a E0 (a, m) = 0|T00 (t, x)|0 dx = 0 2 ωn . 60) does not contribute to the result]. We now consider the quantization of a scalar ﬁeld on the entire axis −∞ < x < ∞. 11) and the commutation relations are as follows: ak , a + k = δ(k − k ), + [ak , ak ] = a+ k , ak = 0. 63) The vacuum state of the scalar ﬁeld on an unbounded axis is deﬁned by the equality ak |0M = 0. 63), we ﬁnd the inﬁnite vacuum energy density of the scalar ﬁeld on the axis: ∞ (0) 0M |T00 (t, x)|0M = 4π −∞ dk ωk .

The experimental conﬁrmation of this prediction is presented in Part III. 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.