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Few-Body Systems

, 59:36 | Cite as

Multi-scale Methods in Quantum Field Theory

  • W. N. Polyzou
  • Tracie Michlin
  • Fatih Bulut
Article
  • 38 Downloads
Part of the following topical collections:
  1. Light Cone 2017

Abstract

Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.

References

  1. 1.
    I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. XLI, 909–996 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    I. Daubechies, Ten Lecture on Wavelets (SIAM, Philadelphia, 1992)CrossRefzbMATHGoogle Scholar
  3. 3.
    S. Singh, G.K. Brennan. arXiv:1606.05068 (2016)
  4. 4.
    K.G. Wilson, Model Hamiltonians for local quantum field theory. Phys. Rev. 140, B445 (1965)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    K.G. Wilson, T.S. Walhout, A. Harindranath, W.-M. Zhang, R.J. Perry, S.D. Glazek, Nonperturbative QCD: a weak-coupling treatment on the light front. Phys. Rev. D 49, 6720 (1994)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    S.D. Głazek, K.G. Wilson, Renormalization of Hamiltonians. Phys. Rev. D 48, 5863 (1993)ADSCrossRefGoogle Scholar
  7. 7.
    F. Bulut, W.N. Polyzou, Wavelets in field theory. Phys. Rev. D 87(11), 116011 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    T. Michlin, W.N. Polyzou, F. Bulut, Multiresolution decomposition of quantum field theories using wavelet bases. Phys. Rev. D95(9), 094501 (2017)ADSGoogle Scholar
  9. 9.
    G. Beylkin, On the representation of operators in bases of compactly supported wavelets. SIAM J. Numer. Anal. 29(6), 1716 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    F. Coester, Bound states of a many particle system. Nucl. Phys. 7, 421 (1958)CrossRefGoogle Scholar
  11. 11.
    F. Wegner, Flow equations for Hamiltonians. Ann. Phys. (Leipzig) 3, 77 (1994)ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The University of IowaIowa CityUSA
  2. 2.Inönü UniversityMalatyaTurkey

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