# Transformation of a Lagrangian

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Starting from the Lagrangian $L=-\partial_{\mu}\phi^{a}\partial^{\mu}\phi^{a}/2-\mu^{2}\phi^{a}\phi^{a}/2-\lambda(\phi^{a}\phi^{a})^{2}/4!$and taking $\mu^{2} \rightarrow -\infty, \lambda \rightarrow \infty$such that $<\phi^{a}\phi^{a}>$is finite and droping any infinite mass fields, I want to get the Lagrangian $L=-f^{2}\partial_{\mu}\sigma^{a}\partial^{\mu}\sigma^{a}/2$where a=1,2,3,4, f a constant with units of mass and we also have the constraint $\Sigma \sigma^{a}\sigma^{a}=1$. Could you give me any hint on how I should start?

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