Renormalization of gauge theories without cohomology

  • Damiano AnselmiEmail author
Regular Article - Theoretical Physics


We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin–Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.


Gauge Theory Gauge Symmetry Master Equation Classical Action Canonical Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The investigation of this paper was carried out as part of a program to complete the book [12], which will be available at once completed. I thank the Perimeter Institute, Waterloo, Ontario, Canada, for hospitality during the first stage of this work and the Physics Department of Fudan University, Shanghai, for hospitality during the final stage of this work.


  1. 1.
    I.A. Batalin, G.A. Vilkovisky, Gauge algebra and quantization. Phys. Lett. B 102, 27–31 (1981) MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    I.A. Batalin, G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators. Phys. Rev. D 28, 2567 (1983). Erratum-ibid. D 30, 508 (1984) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    S. Weinberg, The Quantum Theory of Fields, vol. II (Cambridge University Press, Cambridge, 1995) CrossRefGoogle Scholar
  4. 4.
    D. Anselmi, Master functional and proper formalism for quantum gauge field theory. Eur. Phys. J. C 73, 2363 (2013). arXiv:1205.3862 [hep-th] ADSCrossRefGoogle Scholar
  5. 5.
    G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. I. General theorems. Commun. Math. Phys. 174, 57 (1995). arXiv:hep-th/9405109 MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. II. Application to Yang–Mills theory. Commun. Math. Phys. 174, 116 (1995). arXiv:hep-th/9405194 Google Scholar
  7. 7.
    G. Barnich, F. Brandt, M. Henneaux, General solution of the Wess–Zumino consistency condition for Einstein gravity. Phys. Rev. D 51, R1435 (1995). arXiv:hep-th/9409104 MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    B.L. Voronov, P.M. Lavrov, I.V. Tyutin, Canonical transformations and the gauge dependence in general gauge theories. Sov. J. Nucl. Phys. 36, 292 (1982). Yad. Fiz. 36, 498 (1982) MathSciNetzbMATHGoogle Scholar
  9. 9.
    D. Anselmi, A general field-covariant formulation of quantum field theory. Eur. Phys. J. C 73, 2338 (2013). arXiv:1205.3279 [hep-th] ADSCrossRefGoogle Scholar
  10. 10.
    S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in An Einstein Centenary Survey, ed. by S. Hawking, W. Israel (Cambridge University Press, Cambridge, 1979) Google Scholar
  11. 11.
    D. Anselmi, A master functional for quantum field theory. Eur. Phys. J. C 73, 2385 (2013). arXiv:1205.3584 [hep-th] ADSCrossRefGoogle Scholar
  12. 12.
    D. Anselmi, Renormalization, to appear at

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Dipartimento di Fisica “Enrico Fermi”Università di Pisa, and INFN, Sezione di PisaPisaItaly

Personalised recommendations