By Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, Vladimir Mikhaylovich Mostepanenko
The topic of this e-book is the Casimir influence, a manifestation of zero-point oscillations of the quantum vacuum leading to forces performing among heavily spaced our bodies. For the good thing about the reader, the booklet assembles field-theoretical foundations of this phenomenon, purposes of the overall concept to genuine fabrics, and a finished description of all lately played measurements of the Casimir strength with a comparability among scan and idea. 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 received within the previous couple of years which aren't mirrored in earlier books at the topic, yet that are very promising for primary technology and nanotechnology. The ebook is a special resource of data offering a serious evaluate of all of the major effects and techniques from thousands of magazine papers. It additionally outlines new principles that have now not but been universally accredited yet that are discovering expanding aid from scan.
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Additional info for Advances in the Casimir Effect (International Series of Monographs on Physics)
80) where the dimensionless variable y = k⊥ a/π has been introduced instead of k⊥ . It is notable that E(a) is ﬁnite. 78) ﬁnite. 81) where one more new variable, v = 2πt, has been introduced. 5). 1) for the Casimir pressure. Thus, in the case of the electromagnetic vacuum conﬁned between two parallel ideal-metal planes, the ﬁnal result is obtained by deleting the energy of free Minkowski space using the Abel–Plana formula. This is appropriate for the case under consideration. In more complicated conﬁgurations, however, even after the removal of the contribution from free Minkowski space, the result will in general be inﬁnite, so that some additional renormalization has to be carried out.
In this chapter we brieﬂy present some basic facts related to the quantization procedure for ﬁelds of various spin obeying boundary (or identiﬁcation) conditions. We start with the classical wave equations and then consider various boundary conditions that may be imposed on their solutions. The rest of the chapter is devoted to both the canonical and the path-integral ﬁeld quantization procedure in the presence of boundaries, with stress put on several diﬀerent representations of the vacuum energy.
The vacuum state of the scalar ﬁeld in free Minkowski space is deﬁned by ak |0M = 0. 8) in the vacuum state, (0) 0|T00 (x)|0 = 1 2 3 0 µ=0 ∂ϕ ∂xµ 2 + m2 ϕ2 0 . 54), we obtain 3 ∂ΦJ (r) ∂Φ∗J (r) . 59) This energy density is divergent and, in the general case, depends on the spatial point r. Now we consider the total vacuum energy of the scalar ﬁeld in the quantization volume V . 42) on the boundary surface S. 51), the following result is obtained: 1 (0) E0 = dr 0|T00 (x)|0 = ωJ . 59) has been integrated by parts.
Advances in the Casimir Effect (International Series of Monographs on Physics) by Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, Vladimir Mikhaylovich Mostepanenko