Oct 2018 - Sep 2019

# Loops without loops and the Feynman tree

## by Dr German Rodrigo (IFIC, Valencia)

Europe/London
Description
Quantum field theory is poorly defined in four space-time dimensions
due to unphysical configurations introduced by quantum corrections.
These unphysical configurations lead to the proliferation of
infinities that are usually regulated by modifying the dimensions of
the space-time. In this talk we introduce the loop-tree duality (LTD)
and the four-dimensional unsubtraction (FDU) formalisms. The LTD
allows to rewrite loop scattering amplitudes in terms of connected
tree-level dual amplitudes, and provides a very intuitive view over
the origin of the IR and UV singularities and their interpretation in
terms of causality.  We also comment on its relation to the Feynman’s
Tree Theorem. The FDU allows to perform the summation over soft and
collinear degenerate states from virtual and real configurations by
introducing a suitable mapping of momenta, then avoiding subtractions
in the infrared in such a way that higher order perturbative
calculations can directly be performed in four space-time dimensions.
We illustrate the power of the formalism with benchmark physical
examples.
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