string%20theory
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1: 32.16 Physical Applications
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►Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents.
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►For the Ising model see Barouch et al. (1973), Wu et al. (1976), and McCoy et al. (1977).
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►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
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§20.12(i) Number Theory
… ►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
6: Bibliography P
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Statistical Field Theory.
Addison-Wesley, Reading, MA.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Gauge Field Theories.
Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
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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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Catastrophe Theory and its Applications.
Pitman, London.
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7: 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. …8: Bibliography
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Theory of Incomplete Cylindrical Functions and Their Applications.
Springer-Verlag, Berlin.
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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable.
2nd edition, McGraw-Hill Book Co., New York.
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Unsteady lifting-line theory as a singular-perturbation problem.
J. Fluid Mech 153, pp. 59–81.
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Number Theory.
In The New Encyclopaedia Britannica,
Vol. 25, pp. 14–37.
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Matching higher conserved charges for strings and spins.
J. High Energy Phys. 2004 (3).
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9: Bibliography L
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Essai sur la Théorie des Nombres.
2nd edition, Courcier, Paris.
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Zur Theorie der Gaußschen Summen.
Math. Ann. 57 (4), pp. 554–567 (German).
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Generalized Riemann -function regularization and Casimir energy for a piecewise uniform string.
Phys. Rev. D 44 (2), pp. 560–562.
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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions.
third edition, Springer, New York.
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10: Bibliography D
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Multiplicative Number Theory.
3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
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Pólya’s Theory of Counting.
In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.),
pp. 144–184.
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2.
American Mathematical Society, Providence, RI.
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