# 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} }

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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## References

SHOWING 1-10 OF 48 REFERENCES

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

- Mathematics
- 1985

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…

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

- Mathematics, Physics
- 2002

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

- Mathematics
- 1995

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

- Mathematics
- 2007

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

- Physics
- 2004

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…