Lifshitz formula by spectral summation method

Details Lifshitz formula by spectral summation method Lifshitz formula by spectral summation method

2011-12-12

arxiv.org/abs/1112.2599v1

Physics

Quantum Physics

27 pages, 1 figure, REVTEX4

Scientific paper

The Lifshitz formula is derived by making use of the spectral summation method which is a mathematically rigorous implementation of both the mode-by-mode summation technique and the scattering formalism. The contributions to the Casimir energy of electromagnetic excitations of different types (surface modes, wave-guide modes, and photonic modes) are clearly retraced. A correct transition to imaginary frequencies is accomplished with allowance for all the peculiarities of the pertinent scattering data in the complex $\omega $ plane, including, in particular, the cuts connecting the branch points. A principal novelty in our approach is special choice of appropriate passes in the contour integrals, which are used for transition to imaginary frequencies. As a result, the long standing problem of cuts in the complex $\omega $ plane is solved completely.

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