Casimir operator

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1: 18.38 Mathematical Applications

… ►A further operator, the so-called Casimir operator …

2: 25.17 Physical Applications

… ►This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999). … ►Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect). …

3: Bibliography L

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Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 178 (2), pp. 425–452.

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Notes:

For a Maple implementation of the algorithm given in this paper for Jack and zonal polynomials see Zeilberger (website).

External Links:

ISSN 0010-3616, Link, MathReview (Kazuhiro Hikami), ZentralBlatt

Referenced by:

§35.12.

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BibTeX

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Introduction to spectral theory: selfadjoint ordinary differential operators. Translations of Mathematical Monographs, Vol. 39, American Mathematical Society, Providence, R.I..

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Notes:

Translated from the Russian by Amiel Feinstein

External Links:

MathReview Entry

Referenced by:

§1.18(x).

Encodings:

BibTeX

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Generalized Riemann $\zeta$-function regularization and Casimir energy for a piecewise uniform string. Phys. Rev. D 44 (2), pp. 560–562.

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External Links:

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Referenced by:

§24.18.

Encodings:

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