Friday, 21 February 2020

quantum field theory - Noether current for a local gauge transformation for the Klein-Gordon Lagrangian


The Noether current corresponding to the transformation $\phi \to e^{i\alpha} \phi$ for the Klein-Gordon Lagrangian density


$$\mathcal{L}~=~|\partial_{\mu}\phi|^2 -m^2 |\phi|^2$$


by finding $\delta S$, and setting it to zero. The general formula for a global transformation is


$$j^{\mu}=\frac{\partial \mathcal{L}}{\partial(\partial_{\mu} \phi)}\Delta \phi-\mathcal{J}^{\mu},$$


where $ \partial_{\mu} \mathcal{J}^{\mu}$ is the change in the Lagrangian density due to the transformation. (See Peskin section 2.2).


How do I find the Noether's current corresponding to a local transformation $\phi \to e^{i\alpha(x)}\phi$?




No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...