- #1
spaghetti3451
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The ##1##-point correlation function in any theory, free or interacting, can be made to vanish by a suitable rescaling of the field ##\phi##.
I would like to understand this statement.
With the above goal in mind, consider the following theory:
$$\mathcal{L} = \frac{1}{2}\left((\partial\phi)^{2}-m^{2}\phi^{2}\right)+\frac{g}{2}\phi\partial^{\mu}\phi\partial_{\mu}\phi.$$
What criteria (on the Lagrangian ##\mathcal{L}##) is used to determine the value of the field ##\phi_{0}## such that the transformation ##\phi \rightarrow \phi + \phi_{0}## leads to a vanishing ##1##-point correlation function ##\displaystyle{\langle \Omega | T\{\phi(x_{1}\phi(x_{2})\}| \Omega \rangle}##?
I would like to understand this statement.
With the above goal in mind, consider the following theory:
$$\mathcal{L} = \frac{1}{2}\left((\partial\phi)^{2}-m^{2}\phi^{2}\right)+\frac{g}{2}\phi\partial^{\mu}\phi\partial_{\mu}\phi.$$
What criteria (on the Lagrangian ##\mathcal{L}##) is used to determine the value of the field ##\phi_{0}## such that the transformation ##\phi \rightarrow \phi + \phi_{0}## leads to a vanishing ##1##-point correlation function ##\displaystyle{\langle \Omega | T\{\phi(x_{1}\phi(x_{2})\}| \Omega \rangle}##?