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 performing among heavily spaced our bodies. For the advantage of the reader, the ebook assembles field-theoretical foundations of this phenomenon, functions of the overall idea to genuine fabrics, and a accomplished description of all lately played measurements of the Casimir strength with a comparability among test and conception. there's an pressing desire for a e-book of this sort, given the rise of curiosity in forces originating from the quantum vacuum. a number of new effects were acquired within the previous couple of years which aren't mirrored in past books at the topic, yet that are very promising for basic technology and nanotechnology. The booklet is a different resource of data proposing a severe overview of the entire major effects and methods from 1000's of magazine papers. It additionally outlines new rules that have now not but been universally accredited yet that are discovering expanding aid from scan.
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Additional resources for Advances in the Casimir Effect (International Series of Monographs on Physics)
On two parallel planes or on the four sides of a parallelepiped. 41), one must ﬁnd an explicit expression for the eigenfrequencies ωJ . e. 42) ∂n S we are dealing with Neumann boundary condition. 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.
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 . 13). We recall that L is the inﬁnite length of the axis. 65). 38), we ﬁnally ﬁnd (x) = − c mc2 − 4a 4πa2 ∞ 2µ y 2 − 4µ2 m2 c 4 dy − ey − 1 2a ∞ cos 2kn x .
7) ∂x0 ∂x0 V where V is the quantization volume (free inﬁnite space or some region restricted by boundaries). 4), with Υ = 0. Sometimes what is referred to as the metrical energy–momentum tensor of the scalar ﬁeld is also used (Chernikov and Tagirov 1968, Callan et al. 8) by a 4-divergence (D is the dimensionality of space–time). 10) where ✷ = ∇µ ∇µ , ∇µ is the covariant derivative, the scalar curvature R = Rµµ is the trace of the Ricci tensor, and ξ is the coupling coeﬃcient. 10) is conformally invariant in the limit of zero mass if ξ in the above expression is given by ξ = 1/6 (for D = 4).