Operator approach to analytical evaluation of Feynman diagrams

@article{Isaev2007OperatorAT,
  title={Operator approach to analytical evaluation of Feynman diagrams},
  author={A. P. Isaev},
  journal={Physics of Atomic Nuclei},
  year={2007},
  volume={71},
  pages={914-924}
}
  • A. Isaev
  • Published 4 September 2007
  • Physics
  • Physics of Atomic Nuclei
The operator approach to analytical evaluation of multiloop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration-by-parts method and the method of “uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams… 
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18 Citations
Background Citations
4
Methods Citations
5
Results Citations
1

18 Citations

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References

SHOWING 1-10 OF 48 REFERENCES

Multi-loop Feynman integrals and conformal quantum mechanics

An approach to the calculation of many-loop massless Feynman integrals

A generalization of the identity of dimensionless regular-zation is proposed. The generalization is used to divide the complete set of dimensionally (and analytically) regularized Feynman integrals…

Summation of an infinite series of ladder diagrams

Dimensional regularization and the renormalization group

Recent developments in conformal invariant quantum field theory

A theorem on analytical calculability of 4-loop renormalization group functions

The Bethe-ansatz for N = 4 super Yang-Mills

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector…

On discrete three-dimensional equations associated with the local Yang-Baxter relation

The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a proper generalization to three dimensions of the zero curvature relation. Recently, Korepanov has constructed an infinite…

Magic identities for conformal four-point integrals

We propose an iterative procedure for constructing classes of off-shell four-point conformal integrals which are identical. The proof of the identity is based on the conformal properties of a…

INTEGRABILITY IN QCD AND BEYOND

Yang–Mills theories in four space–time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns…