I know that the effective action can be written as a double expansion in derivatives and loop (h-bar). For example, take the effective action for a real scalar field:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma[\phi]=\int d^4x\left[V_\text{eff}(\phi)+\frac{1}{2}Z(\phi)\partial_\mu\phi\partial^\mu\phi+\mathcal{O}(\partial^4)+\ldots\right] [/tex]

[tex]=\int d^4x\left[V^{(0)}(\phi)+\hbar V^{(1)}(\phi)+\ldots+\frac{1}{2}(1+\hbar Z^{(1)}(\phi)+\ldots)\partial_\mu\phi\partial^\mu\phi+\mathcal{O}(\partial^4)+\ldots\right] [/tex]

I am familiar with the techniques of getting the terms with zero derivatives (effective potential) to the desired order in the loop expansion (path integral method, tadpole method, etc...) -- this is fairly standard.

But, are there techniques of reliably getting closed-form expressions for the Z-functions in front of derivative terms? (preferably using path integrals)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivative Terms of Effective Action

**Physics Forums | Science Articles, Homework Help, Discussion**