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quantum field theory


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1: 25.17 Physical Applications
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). …
2: 23.21 Physical Applications
§23.21 Physical Applications
  • Quantum field theory. See Witten (1987).

  • 3: Bibliography I
  • C. Itzykson and J. B. Zuber (1980) Quantum Field Theory. International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.
  • 4: Bibliography W
  • E. Witten (1987) Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (4), pp. 525–536.
  • 5: 22.19 Physical Applications
    plays a prototypal role in classical mechanics (Lawden (1989, §5.2)), quantum mechanics (Schulman (1981, Chapter 29)), and quantum field theory (Pokorski (1987, p. 203), Parisi (1988, §14.6)). …
    6: 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.
  • 7: 15.18 Physical Applications
    More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).
    8: 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.
  • E. W. Leaver (1986) Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics. J. Math. Phys. 27 (5), pp. 1238–1265.
  • 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).
  • 9: 9.16 Physical Applications
    Airy functions are applied in many branches of both classical and quantum physics. … The KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics. … An example from quantum mechanics is given in Landau and Lifshitz (1965), in which the exact solution of the Schrödinger equation for the motion of a particle in a homogeneous external field is expressed in terms of Ai ( x ) . …This reference provides several examples of applications to problems in quantum mechanics in which Airy functions give uniform asymptotic approximations, valid in the neighborhood of a turning point. A study of the semiclassical description of quantum-mechanical scattering is given in Ford and Wheeler (1959a, b). …
    10: Mourad E. H. Ismail
    Ismail has published numerous papers on special functions, orthogonal polynomials, approximation theory, combinatorics, asymptotics, and related topics. His well-known book Classical and Quantum Orthogonal Polynomials in One Variable was published by Cambridge University Press in 2005 and reprinted with corrections in paperback in Ismail (2009). …  Rahman), Fields Institute Communications, v. … Suslov), Kluwer Academic Publishers, 2001; Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (with F. … Garvan), Kluwer Academic Publishers, 2001; and Theory and Applications of Special Functions: A volume dedicated to Mizan Rahman (with E. …