Skip to main content
SpringerLink
Log in

Multi-scale Methods in Quantum Field Theory

  • Published:
Few-Body Systems Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. XLI, 909–996 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. I. Daubechies, Ten Lecture on Wavelets (SIAM, Philadelphia, 1992)

    Book  MATH  Google Scholar 

  3. S. Singh, G.K. Brennan. arXiv:1606.05068 (2016)

  4. K.G. Wilson, Model Hamiltonians for local quantum field theory. Phys. Rev. 140, B445 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  6. S.D. Głazek, K.G. Wilson, Renormalization of Hamiltonians. Phys. Rev. D 48, 5863 (1993)

    Article  ADS  Google Scholar 

  7. F. Bulut, W.N. Polyzou, Wavelets in field theory. Phys. Rev. D 87(11), 116011 (2013)

    Article  ADS  Google Scholar 

  8. T. Michlin, W.N. Polyzou, F. Bulut, Multiresolution decomposition of quantum field theories using wavelet bases. Phys. Rev. D95(9), 094501 (2017)

    ADS  Google Scholar 

  9. G. Beylkin, On the representation of operators in bases of compactly supported wavelets. SIAM J. Numer. Anal. 29(6), 1716 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. F. Coester, Bound states of a many particle system. Nucl. Phys. 7, 421 (1958)

    Article  Google Scholar 

  11. F. Wegner, Flow equations for Hamiltonians. Ann. Phys. (Leipzig) 3, 77 (1994)

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Iowa, Iowa City, USA

    W. N. Polyzou & Tracie Michlin

  2. Inönü University, Malatya, Turkey

    Fatih Bulut

Authors
  1. W. N. Polyzou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tracie Michlin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fatih Bulut
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. N. Polyzou.

Additional information

W.P. acknowledges the generous support of the U.S. Department of Energy, grant number DE-SC0016457.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polyzou, W.N., Michlin, T. & Bulut, F. Multi-scale Methods in Quantum Field Theory. Few-Body Syst 59, 36 (2018). https://doi.org/10.1007/s00601-018-1357-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-018-1357-z

Search

Navigation