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Dynamics VIII: Interacting fields: perturbative aspects

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199573264
eISBN:
9780191743313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573264.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the perturbative aspects of interacting field theory: namely, the techniques appropriate for studying those aspects of local quantum field theories which emerge from a formal ... More


Quantum field theory (QFT)—built-in combinatorics

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

We briefly exhibit in this chapter the mathematical formalism of QFT, which actually has a non-trivial combinatorial backbone. The QFT setting can be understood as a quantum description of particles ... More


The perturbative expansion of tensor models

Razvan Gurau

in Random Tensors

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198787938
eISBN:
9780191829918
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198787938.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents the perturbative expansion of invariant tensor measures in terms of Feynman graphs. It is shown that, assuming that the perturbation and the Gaussian part scale at the same rate ... More


Tree weights and renormalization in QFT

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter we define specific tree weights which appear natural when considering a certain approach to non-perturbative renormalization in QFT, namely the constructive renormalization. Several ... More


Combinatorial QFT and the Jacobian Conjecture

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The Jacobian Conjecture states that any complex n-dimensional locally invertible polynomial system is globally invertible with polynomial inverse. In 1982, Bass et al. proved an important reduction ... More


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