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1: 32.16 Physical Applications

… ►For the Ising model see Barouch et al. (1973), Wu et al. (1976), and McCoy et al. (1977). … ►For applications in string theory see Seiberg and Shih (2005).

2: 19.35 Other Applications

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§19.35(ii) Physical

►Elliptic integrals appear in lattice models of critical phenomena (Guttmann and Prellberg (1993)); theories of layered materials (Parkinson (1969)); fluid dynamics (Kida (1981)); string theory (Arutyunov and Staudacher (2004)); astrophysics (Dexter and Agol (2009)). …

3: 20.12 Mathematical Applications

… ►This ability to uniformize multiply-connected spaces (manifolds), or multi-sheeted functions of a complex variable (Riemann (1899), Rauch and Lebowitz (1973), Siegel (1988)) has led to applications in string theory (Green et al. (1988a, b), Krichever and Novikov (1989)), and also in statistical mechanics (Baxter (1982)). …

4: 21.9 Integrable Equations

§21.9 Integrable Equations

►Riemann theta functions arise in the study of integrable differential equations that have applications in many areas, including fluid mechanics (Ablowitz and Segur (1981, Chapter 4)), magnetic monopoles (Ercolani and Sinha (1989)), and string theory (Deligne et al. (1999, Part 3)). …

5: 23.21 Physical Applications

§23.21 Physical Applications

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String theory. See Green et al. (1988a, §8.2) and Polchinski (1998, §7.2).

6: 5.20 Physical Applications

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Elementary Particles

►Veneziano (1968) identifies relationships between particle scattering amplitudes described by the beta function, an important early development in string theory. …

7: Bibliography P

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String Theory: An Introduction to the Bosonic String, Vol. I. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-63303-6, MathReview (Angel Maria Uranga), ZentralBlatt

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3rd item.

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8: Bibliography D

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Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.

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Notes:

Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997

External Links:

ISBN 0-8218-1198-3, MathReview, ZentralBlatt

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§21.9.

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9: 28.33 Physical Applications

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McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.

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Aly et al. (1975) for scattering theory.

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Fukui and Horiguchi (1992) for quantum theory.

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10: Bibliography L

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The Classical Theory of Fields. Pergamon Press, Oxford.

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Notes:

Revised second edition. Course of Theoretical Physics, Vol. 2. Translated from the Russian by Morton Hamermesh

External Links:

MathReview (E. L. Hill), ZentralBlatt

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§9.16.

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Quantum Mechanics: Non-relativistic Theory. Pergamon Press Ltd., Oxford.

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Notes:

Revised second edition. Course of Theoretical Physics, Vol. 3. Translated from the Russian by J. B. Sykes and J. S. Bell

External Links:

MathReview, ZentralBlatt

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§9.16.

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Essai sur la Théorie des Nombres. 2nd edition, Courcier, Paris.

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§27.2(i).

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Zur Theorie der Gaußschen Summen. Math. Ann. 57 (4), pp. 554–567 (German).

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External Links:

ISSN 0025-5831, Document, MathReview Entry, ZentralBlatt

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§20.11(i).

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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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Document

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§24.18.

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