Tree Quantum Field Theory

We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and...

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Bibliographic Details
Published in:arXiv.org 2008-07
Main Authors: Gurau, R, Magnen, J, Rivasseau, V
Format: Article
Language:English
Subjects:
Differential equations
Feynman diagrams
Field theory
Formalism
Magnetic fields
Polynomials
Quantum field theory
Quantum theory
Online Access:Get full text
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Summary:We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively {\it differential} renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension.
ISSN:2331-8422
DOI:10.48550/arxiv.0807.4122