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Summary

We introduce generalized cuts for Feynman integrals, transforming integration domains into finite volumes. This method simplifies calculations and offers new perspectives on maximal cuts and linear relations among them.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Mathematical methods in physics

Background:

  • Feynman integrals are crucial in quantum field theory but often involve complex integration domains.
  • Existing methods for analyzing Feynman integrals can be computationally intensive and challenging to generalize.

Purpose of the Study:

  • To develop a novel construction of generalized cuts for Feynman integrals.
  • To transform integration domains into full-dimensional spaces with finite volumes.
  • To provide new formulations for maximal cuts and derive relations among them.

Main Methods:

  • Defining generalized cuts as an operation on the domain of Feynman parametric integrals.
  • Utilizing on-shell conditions to modify integration domain boundaries.
  • Applying the inclusion-exclusion principle for deriving linear relations.

Main Results:

  • A new construction of generalized cuts for Feynman integrals is proposed.
  • Integration domains are modified to become full-dimensional spaces with finite volumes.
  • New formulations of maximal cuts and a simple derivation of linear relations among cuts are presented.

Conclusions:

  • The proposed method offers a more manageable approach to analyzing Feynman integrals.
  • This construction simplifies the study of maximal cuts and their interrelations.
  • The technique provides a powerful tool for theoretical physics research.