By Bordag M., Klimchitskaya G.L., Mohideen U., Mostepanenko V.M.
The topic of this publication is the Casimir impression, 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, functions of the overall thought to genuine fabrics, and a entire 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 kind, 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 past books at the topic, yet that are very promising for basic technological know-how and nanotechnology. The ebook is a different resource of knowledge featuring a serious overview of the entire major effects and methods 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 resources for Advances in the Casimir Effect
2) ✷2 ϕ(t, x) = 2 c ∂t2 ∂x2 Note that this scalar ﬁeld in two-dimensional space–time is dimensionless. Let us consider the properties of the scalar ﬁeld deﬁned on an interval 0 < x < a with Dirichlet boundary conditions imposed at its ends, ϕ(t, 0) = ϕ(t, a) = 0. 3) Next we shall consider the scalar ﬁeld along the entire axis −∞ < x < ∞. In both cases our primary goal is to ﬁnd the spectrum of scalar oscillations. 4) where x0 = x0 = ct. 1), it follows that (f, g) does not depend on time. 5) is given by 1/2 c aωn ϕ(±) n (t, x) = e∓iωn t sin kn x.
5), obtained for the vacuum energy of the electromagnetic ﬁeld between ideal-metal planes. 19) does not depend on the form of cutoﬀ function used. 19) retains its validity for any regularization function satisfying some general requirements. The magnitude of the Casimir energy E(a) increases monotonically as the boundary points approach each other. 19), the Casimir force acting between the boundary points of the interval is F (a) = − ∂E(a) π c =− . 1) between two parallel, ideal-metal planes. 18) is a typical example of what are commonly referred to as subtraction procedures, used in quantum ﬁeld theories in order to remove inﬁnities The Abel–Plana formula and regularization 21 from divergent expectation values of physical quantities.
47) This is usually referred to as the Coulomb gauge. 48) where the index “t” marks the components of E and AJ tangential to the surface. 44). 71). Here, we have assumed that both the electric ﬁeld and the magnetic induction vary sinusoidally in time as exp(−iωJ t), which is always true for any static conﬁguration of boundary surfaces. 48) is of Dirichlet type. Thus, the same elliptic boundary problem as in the case of a scalar ﬁeld is relevant to the electromagnetic ﬁeld. In the next chapters of Part I, the solutions of various boundary problems will be presented for a number of conﬁgurations of boundary surfaces.