By Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, Vladimir Mikhaylovich Mostepanenko
The topic of this publication is the Casimir influence, 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 booklet assembles field-theoretical foundations of this phenomenon, purposes of the final conception to genuine fabrics, and a finished description of all lately played measurements of the Casimir strength with a comparability among test and concept. there's an pressing desire for a booklet of this sort, given the rise of curiosity in forces originating from the quantum vacuum. quite a few 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 technology and nanotechnology. The publication is a distinct resource of data offering a severe review of all of the major effects and ways from thousands of magazine papers. It additionally outlines new rules that have now not but been universally accredited yet that are discovering expanding help from scan.
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Extra resources for Advances in the Casimir Effect (International Series of Monographs on Physics)
However, it is preferable to perform the quantization of the electromagnetic ﬁeld in terms of the vector potential Aµ . First, we choose the Coulomb gauge, where A0 (x) = 0 and divA(x) = 0, as was done in the previous section devoted to the discussion of boundary conditions. 22) takes the form ∂ 2 A(x) − ∇2 A(x) = 0. 45) with appropriate boundary conditions. 64) are orthonormal, satisfying the equation V dr A∗J (r)AJ (r) = 4πδJJ . 66) Now we assume that the boundaries under consideration allow the deﬁnition (λ) of two orthonormal polarization vectors J : (λ) J · (λ ) J = δλλ , λ, λ = 1, 2.
In Parts II and III, which deal with real materials and experiments, the fundamental constants in all mathematical expressions are explicitly indicated. The electromagnetic equations are written in the Gaussian system of units. Some values of experimentally measured quantities and simple formulas are given in the International System (SI) of units. This is indicated in the text. When this does not create confusion, operators and c-functions are notated in a similar way. Other special notations particular to a chapter are introduced where necessary.
3 FIELD QUANTIZATION AND VACUUM ENERGY IN THE PRESENCE OF BOUNDARIES From the standpoint of quantum ﬁeld theory, the Casimir eﬀect is related to the vacuum polarization arising in quantization volumes restricted by boundaries or in spaces with nontrivial topology. Both boundaries and a nontrivial topology of space–time can be considered as classical external conditions, on which background the ﬁeld quantization should be performed. In this chapter we brieﬂy present some basic facts related to the quantization procedure for ﬁelds of various spin obeying boundary (or identiﬁcation) conditions.
Advances in the Casimir Effect (International Series of Monographs on Physics) by Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, Vladimir Mikhaylovich Mostepanenko