By Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, Vladimir Mikhaylovich Mostepanenko
The topic of this booklet 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 publication assembles field-theoretical foundations of this phenomenon, functions of the final thought 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 want for a ebook of this sort, given the rise of curiosity in forces originating from the quantum vacuum. quite a few new effects were got within the previous couple of years which aren't mirrored in prior books at the topic, yet that are very promising for primary technology and nanotechnology. The e-book is a special resource of data featuring a serious overview of the entire major effects and ways from hundreds of thousands of magazine papers. It additionally outlines new principles that have no longer but been universally permitted yet that are discovering expanding aid from scan.
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Extra resources for Advances in the Casimir Effect (International Series of Monographs on Physics)
16), the vacuum energy for such an interval is (δ) (δ) E0M (a) = E0M a a= . 3). 15), diverging when δ goes to zero. 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 . 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.
38), does not contain a contribution linear in the mass. The physical explanation for this fact is that the space with the topology of a circle does not 26 Simple models of the Casimir eﬀect contain boundary points and hence the vacuum energy does not contain their energy. 47) leads to (Mamayev and Trunov 1979a) c ∞ y dy π c E(a, 0) = E(a) = − =− . e. the Casimir energy is exponentially small. At the end of this section, we brieﬂy discuss what are referred to as antiperiodic conditions imposed on a scalar ﬁeld, ϕ(t, x + a) = −ϕ(t, x).
The vacuum energy density is deﬁned as the expectation value of the energy density operator of the quantized ﬁeld in the vacuum state. Here, we present only the most elementary aspects of ﬁeld quantization for a scalar ﬁeld in two-dimensional space–time. We save the more general discussion of ﬁeld quantization in the presence of boundaries for Chapter 3. 7). 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.