Oct 2018 - Sep 2019

Loops without loops and the Feynman tree

by Dr German Rodrigo (IFIC, Valencia)

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  
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