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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
§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: 5.20 Physical Applications
Elementary Particles
Veneziano (1968) identifies relationships between particle scattering amplitudes described by the beta function, an important early development in string theory. …
6: 23.21 Physical Applications
§23.21 Physical Applications
  • String theory. See Green et al. (1988a, §8.2) and Polchinski (1998, §7.2).

  • 7: Bibliography P
  • J. Polchinski (1998) String Theory: An Introduction to the Bosonic String, Vol. I. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • 8: Bibliography D
  • P. Deligne, P. Etingof, D. S. Freed, D. Kazhdan, J. W. Morgan, and D. R. Morrison (Eds.) (1999) Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.
  • 9: 28.33 Physical Applications
  • McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.

  • Aly et al. (1975) for scattering theory.

  • Fukui and Horiguchi (1992) for quantum theory.

  • 10: Bibliography L
  • L. D. Landau and E. M. Lifshitz (1962) The Classical Theory of Fields. Pergamon Press, Oxford.
  • L. D. Landau and E. M. Lifshitz (1965) Quantum Mechanics: Non-relativistic Theory. Pergamon Press Ltd., Oxford.
  • A. M. Legendre (1808) Essai sur la Théorie des Nombres. 2nd edition, Courcier, Paris.
  • M. Lerch (1903) Zur Theorie der Gaußschen Summen. Math. Ann. 57 (4), pp. 554–567 (German).
  • X. Li, X. Shi, and J. Zhang (1991) Generalized Riemann ζ -function regularization and Casimir energy for a piecewise uniform string. Phys. Rev. D 44 (2), pp. 560–562.