# Representations of scalar fields from the expressions of fields

Consider scalar field $$\phi(x)$$, when we quantize this scalar field we get an expression in terms of creation and annihilation operators as $$\phi(x) = \sum c(p)({ae^{ipx} + a^\dagger e^{-ipx}} )$$. If I have a field with $$a(k) \to e^{i\theta}a(k)$$ . How do I find representations of the changed field ?

• Do you have a concrete example where this question came up? Because I don't quite understand what you mean... – MannyC Mar 8 at 6:23
• The only thing I can really say is the number operator N is invariant. It would be nice to have a Lagrangian. – Cinaed Simson Mar 10 at 1:03