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Generalized Cuts of Feynman Integrals in Parameter Space
1Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA and School of Mathematics and Hamilton Mathematics Institute, Trinity College, Dublin 2, Ireland.
Physical Review Letters
|September 18, 2023
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.
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.
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