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

The topic of this publication is the Casimir impression, 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 e-book assembles field-theoretical foundations of this phenomenon, functions of the overall idea to genuine fabrics, and a complete description of all lately played measurements of the Casimir strength with a comparability among test and conception. there's an pressing want for a e-book of this kind, given the rise of curiosity in forces originating from the quantum vacuum. a variety of new effects were got 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 publication is a special resource of data providing a severe evaluate of all of the major effects and techniques from enormous quantities of magazine papers. It additionally outlines new principles that have now not but been universally authorised yet that are discovering expanding aid from test.

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**Sample text**

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 . 13). We recall that L is the inﬁnite length of the axis. 65).

71) can be viewed as an ideal case of the interaction of real metal surfaces with an electromagnetic ﬁeld. e. by the penetration of the electromagnetic ﬁeld into the metal to a characteristic length scale given by the skin depth. This problem becomes particularly involved at nonzero temperature (see Chapters 12 and 14). 4), where J is the photon wave vector. e. without boundaries), J = k = (k 1 , k 2 , k 3 ), where all k i are continuous. In the presence of metal planes, this is not so, however.

NonEuclidean), identiﬁcation conditions may be imposed on ﬁelds. These are similar to boundary conditions for classical material boundaries. The simplest example is provided by the interval 0 ≤ x ≤ a whose initial and end points are identiﬁed by means of the following periodic conditions: ϕ(t, 0) = ϕ(t, a), ∂x ϕ(t, x)|x=0 = ∂x ϕ(t, x)|x=a . 42) is a circle of circumference a. Both manifolds are ﬂat, but their topologies are diﬀerent. Interval I [Fig. 42) possesses the topology of a circle S 1 [Fig.