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

The topic of this e-book 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 good thing about the reader, the e-book assembles field-theoretical foundations of this phenomenon, purposes of the final idea to actual fabrics, and a accomplished description of all lately played measurements of the Casimir strength with a comparability among scan and conception. there's an pressing want for a ebook of this sort, given the rise of curiosity in forces originating from the quantum vacuum. a variety of new effects were acquired within the previous few years which aren't mirrored in prior books at the topic, yet that are very promising for basic technology and nanotechnology. The booklet is a distinct resource of knowledge offering a serious review of the entire major effects and ways from countless numbers of magazine papers. It additionally outlines new rules that have no longer but been universally authorized yet that are discovering expanding aid from test.

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Here and below, we shall also use the notation x1 ≡ x, x2 ≡ y, x3 ≡ z and k 1 ≡ kx , k 2 ≡ ky , k 3 ≡ kz where there is no cause for confusion with four-dimensional quantities. Let us choose Cartesian coordinates with the z-axis perpendicular to the planes. Then the components kx , ky remain continuous, but the component kz = kzn = πn/a, n = 0, ±1, ±2, becomes discrete. 7) for a scalar ﬁeld on an interval, here n can be a negative integer, which takes the two photon polarizations into account. 2, where the complete orthonormal set of solutions of the wave equation between the two parallel planes is explicitly presented).

The operators an and a+ n are the annihilation and creation operators of a scalar particle with quantum number n. They obey the standard commutation relations an , a+ n = δnn , + [an , an ] = a+ n , an = 0. 57) The vacuum state |0 of the ﬁeld on an interval is deﬁned by an |0 = 0. 58) The energy density operator of the scalar ﬁeld in two-dimensional space–time is given by the 00-component of the energy–momentum tensor (0) T00 (t, x) = c 2 1 m 2 c2 2 2 [∂t ϕ(t, x)] + [∂x ϕ(t, x)] + 2 ϕ2 (t, x) .

The use of corrugated surfaces allows one to study the nontrivial boundary properties of the Casimir force and to demonstrate for the ﬁrst time the physical phenomenon of the lateral Casimir force, which was previously predicted theoretically (see Chapter 17). Chapter 22 discusses measurements of the Casimir–Polder force in the experiments on Bose–Einstein condensation and quantum reﬂection. Special attention is paid to an experiment where the thermal Casimir–Polder force was measured for the ﬁrst time (Obrecht et al.

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