How does the residue factorization form arise in BCFW recursion in QFT?

  • Context: Undergrad 
  • Thread starter Thread starter Lapidus
  • Start date Start date
  • Tags Tags
    Recursion Relation
Click For Summary
SUMMARY

The discussion centers on the residue factorization form in BCFW recursion within Quantum Field Theory (QFT). Key references include Britto's 2011 paper, Eden et al.'s "The Analytic S-matrix," and Weinberg's "The Quantum Theory of Fields Vol 1." The residue, defined as the numerator of a rational function with a simple pole, can be demonstrated through both S-matrix properties and local field theoretic proofs. The factorization of amplitudes at simple poles is established through these rigorous methodologies.

PREREQUISITES
  • Understanding of BCFW recursion in Quantum Field Theory
  • Familiarity with S-matrix properties: analyticity, unitarity, and cluster decomposition
  • Knowledge of residue theory in complex analysis
  • Experience with Quantum Field Theory texts, particularly Weinberg's and Zee's works
NEXT STEPS
  • Study Britto's 2011 paper on BCFW recursion for detailed insights
  • Review Eden et al.'s "The Analytic S-matrix" for foundational proofs
  • Examine Weinberg's "The Quantum Theory of Fields Vol 1" for local field theoretic approaches
  • Explore the review by Conde for contemporary discussions on residue factorization
USEFUL FOR

Researchers, graduate students, and theoretical physicists specializing in Quantum Field Theory, particularly those focused on scattering amplitudes and BCFW recursion techniques.

Lapidus
Messages
344
Reaction score
12
Below is a snipet from http://file:///C:/Users/Christian.Hollersen/Downloads/Britto_2011_2%20(1).pdf of Britto. Similar explanation can be found in the QFT books of Zee, Schwarz or the Scattering Amplitude text of Huang. Or any other text that covers BCFW recursion. My dumb question: how and why does the residue at this pole take this funny factorization form? (For clarifcation: residue is the just the word QFT people use for the numerator of a rational function with a simple pole, right?)

bcwf.PNG


Thank you!
 
Last edited by a moderator:
Physics news on Phys.org
There are at least two ways to show the factorization of amplitudes on simple poles. An ancient proof using only properties of the S-matirx (analyticity, unitarity and cluster decomposition) can be found in Eden et al. "The Analytic S-matrix" sec. 4.5. For a more recent discussion see the nice review by Conde

http://pos.sissa.it/archive/conferences/201/005/Modave 2013_005.pdf

Alternatively there is a more local field theoretic proof given in Weinberg "The Quantum Theory of Fields Vol 1." sec. 10.2.