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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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