The geometric $\beta$-function in curved space-time under operator regularization

Preprint English OPEN
Agarwala, Susama;
  • Subject: Mathematical Physics
    arxiv: Mathematics::Differential Geometry

In this paper, I compare the generators of the renormalization group flow, or the geometric $\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\beta$-function for a scalar field theory on ... View more
  • References (25)
    25 references, page 1 of 3

    [1] Matilde Marcolli Alain Connes, Noncommutative geometry, Quantum Fields, and motives, American Mathematical Society, USA, 2008.

    [2] Christoph Bergbauer and Dirk Kreimer, Hopf algebras in renormalization theory: Locality and DysonSchwinger equations from Hochschild cohomology, IRMA Lectures in Mathematics and Theoretical Physics 10 (2006), 133 - 164, arXiv:hep-th/0506190v2.

    [3] Alain Connes and Dirk Kreimer, Renormalization in Quantum Field Theory and the Riemann-Hilbert problem I: The Hopf algebra structure of graphs and the main theorem, Communications in Mathematical Physics 210 (2001), 249-273, arXiv:hep-th/9912092v1.

    [4] , Renormalization in Quantum Field Theory and the Riemann-Hilbert problem II: The β function, diffeomorphisms and renormalization group, Communications in Mathematical Physics 216 (2001), 215- 241, arXiv:hep-th/0003188v1.

    [5] Alain Connes and Matilde Marcolli, From physics to number theory via noncommutative geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory, arXiv:hepth/0411114v1, 2004.

    [6] , Quantum Fields and motives, Journal of Geometry and Physics 56 (2006), 55-85.

    [7] Kurusch Ebrahimi-Fard and Dominique Manchon, On matrix differential equations in the Hopf algebra of renormalization, Advances in Theoretical and Mathematical Physics 10 (2006), 879-913, arXiv:mathph/0606039v2.

    [8] Kurush Ebrahimi-Fard and Dirk Kreimer, Hopf algebra approach to Feynman diagram calculations, Journal of physics A 38 (2006), R385 - R406, arXiv:hep-th/0510202v2.

    [9] E. Elizalde, Zeta regularization techniques with applications, World Scientific, 1994.

    [10] David Gross, Renormalization groups, In Quantum Fields and Strings: A Course for Mathematicians (Pierre Deligne, David Kazhkan, Pavel Etingof, John W. Morgan, Daniel S. Freed, David R. Morrison, Lisa C. Jeffrey, and Edward Witten, eds.), vol. 1, American Mathematical Society, Providence, RI, 1999, pp. 551-596.

  • Metrics
Share - Bookmark