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Causality and Loop-Tree Duality at Higher Loops.

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Summary
This summary is machine-generated.

We connect l-loop Feynman integrals to phase space integrals using spanning trees. A new formula ensures correct causality via modified iδ prescriptions for propagators in quantum field theory calculations.

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Area of Science:

  • Quantum Field Theory
  • High Energy Physics
  • Mathematical Physics

Background:

  • Feynman integrals are essential for calculating probabilities in quantum field theory.
  • Determining the correct prescription for propagators, especially in multi-loop integrals, is crucial for physical consistency.

Purpose of the Study:

  • To establish a novel relationship between l-loop Feynman integrals and phase space integrals.
  • To develop a method for correctly implementing causality in these calculations.

Main Methods:

  • Representing l-loop Feynman integrals as sums of phase space integrals.
  • Utilizing the spanning tree decomposition of the Feynman graph.
  • Deriving a modified iδ prescription for tree propagators.

Main Results:

  • A direct correspondence between l-loop Feynman integrals and sums of phase space integrals is established.
  • The integrands of these phase space integrals are determined by the spanning trees of the Feynman graph.
  • A simple and general formula for the correct iδ prescription, ensuring causality, is presented.

Conclusions:

  • The spanning tree method provides a powerful tool for evaluating complex Feynman integrals.
  • The derived iδ prescription resolves issues of causality in multi-loop calculations.
  • This work offers a simplified approach to handling Feynman integrals in quantum field theory.