master field

From Physics wiki

Jump to: navigation, search
This page may need to be improved by providing references to primary sources. More than likely this is because it contains references to derived works when the original works are likely still available. Please consult the editing guidelines for more information.

The large N limit of some gauge theories often behaves like the classical limit of some theory. For instance, the expectation value of gauge-invariant operators factorizes like

\left\langle \mathcal{O}_1 \mathcal{O}_2 \right\rangle \sim \left\langle \mathcal{O}_1\right\rangle \left\langle \mathcal{O}_2\right\rangle + O\left(\tfrac{1}{N}\right)\,.

The genus expansion of Feynman diagrams resembles the normal loop expansion, with \hbar\, replaced by \tfrac{1}{N}\,. In the strict N \to \infty\, limit, the path integral is dominated by a classical field configuration or saddle point, which is referred to as the master field. Knowledge of this field allows us to compute gauge-invariant quantities exactly, without functional integration.

References

[1]

  1. ↑ Rajesh Gopakumar (1996). "The Master Field in Generalised QCD2". Nucl.Phys. B 471: 246-262. arXiv:hep-th/9512225v1. DOI:10.1016/0550-3213(96)00191-5. 
Retrieved from "http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/master_field"
Personal tools