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in our lecture, we computed [tex] \beta^{\overline{MS}} , \gamma_m^{\overline{MS}}[/tex] for [tex] - \frac{\lambda}{4!} \phi^4 [/tex] Theory.

These are:

[tex]

\beta^{\overline{MS}} (\lambda_{\overline{MS}}) = b_1 \lambda_{\overline{MS}}^2 + O(\lambda_{\overline{MS}}^3) [/tex]

[tex]

\gamma_m^{\overline{MS}} (\lambda_{\overline{MS}}) = d_1 \lambda_{\overline{MS}} + O(\lambda_{\overline{MS}}^2)

[/tex]

Is there any change, if one goes to a [tex] - \frac{\lambda}{4!} \phi^2 [/tex] Theory?

I think that the Lagrangian changes to:

[tex] L = \frac{1}{2} Z (\partial_{\mu} \phi_R)^2 - \frac{1}{2} m_0^2 Z \phi_R^2 - \frac{\lambda_0}{4!} Z \phi_R^2[/tex]

But that has no effect on computing the beta- and gamma-function. Am I right?

Regards,

Mr. Fogg