nLab Tr(ϕ³)

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

 Idea

Tr(ϕ 3)Tr(\phi^3) is a variant of Yang-Mills theory consisting of spin-zero gluons. The name of the theory comes from the cubic self-interaction term Tr(ϕ 3)Tr(\phi^3) which appears in the Lagrangian of the theory:

=Tr(ϕ) 2+m 2Tr(ϕ 2)+gTr(ϕ 3). \mathcal{L} \;=\; Tr(\partial \phi)^2 + m^2 Tr(\phi^2) + g Tr(\phi^3) \,.

The theory has been used by Nima Arkani-Hamed and collaborators to extend techniques of scattering amplitudes to non-supersymmetric Yang-Mills theory.

References

Discussion on the relation between the nonlinear σ \sigma -model and Tr(ϕ 3)Tr(\phi^3):

Discussion on cosmohedra in Tr(ϕ 3)Tr(\phi^3):

Last revised on June 4, 2025 at 16:56:10. See the history of this page for a list of all contributions to it.