In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x \left[\frac12(\partial_\mu\phi)^2-U(\phi)\right],$$
where $U(x)$ is a general self-interaction potential. Then, the authors proceed by saying that for the standard $\phi^4$ theory, the interaction potential can be written as
$$U(\phi)= \frac{1}{8} \phi^2 (\phi -2)^2.$$

Why is this so? What is the significance of the cubic term present?

In this question Willie Wong answered by setting $\psi = \phi - 1$, why is that? Or why is this a gauge transformation?
Does anyone have better argument to understand the interection potential?

This post imported from StackExchange Physics at 2014-03-22 17:08 (UCT), posted by SE-user Unlimited Dreamer