By Bordag M., Klimchitskaya G.L., Mohideen U., Mostepanenko V.M.
The topic of this ebook 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 ebook assembles field-theoretical foundations of this phenomenon, functions of the final idea to genuine fabrics, and a finished description of all lately played measurements of the Casimir strength with a comparability among test and thought. there's an pressing desire for a ebook of this kind, given the rise of curiosity in forces originating from the quantum vacuum. various new effects were acquired within the previous few years which aren't mirrored in past books at the topic, yet that are very promising for primary technological know-how and nanotechnology. The e-book is a different resource of data proposing a serious review of the entire 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 help from test.
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Additional info for Advances in the Casimir Effect
39) together with the boundary conditions imposed on the function ΦJ (r) deﬁnes a standard elliptic problem for the self-adjoint operator ∆. The most frequently used boundary condition is the Dirichlet one, ΦJ (r)|S = 0. 41) Physically, this means that the boundary surface is totally impermeable to the ﬁeld. e. on two parallel planes or on the four sides of a parallelepiped. 41), one must ﬁnd an explicit expression for the eigenfrequencies ωJ . e. 42) ∂n S we are dealing with Neumann boundary condition.
38) where 2πt ≡ y and πA = mca/ ≡ µ (the latter parameter has the meaning of a dimensionless mass). 38) is associated with the total energy of the boundary points. It does not depend on a and hence does not contribute to the Casimir force. 19). e. the distance-dependent term is exponentially small. The same is obtained for a conﬁguration of two parallel planes in three-dimensional space–time for massive ﬁelds with spins 0, 1/2, and 1. This is valid, however, only for plane 24 Simple models of the Casimir eﬀect boundaries.
15) for an interval constrained by the boundaries. This leads to the ﬁnite quantity (δ) (δ) E (δ) (a) ≡ E0 (a) − E0M (a) = − π c + O(δ 2 ). 18) By removing the regularization, we obtain the Casimir energy for the scalar ﬁeld on an interval, π c E(a) = lim E (δ) (a) = − . 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.