QFTs without Lagrangian

Question

I have been reading other questions in this site, but I have not found answers to all my questions about theories without Lagrangians.

What do we mean exactly when we say that they do not have a Lagrangian? Do they still have an action but this action cannot be defined as the integral of a local Lagrangian? Is it then that they do not have a local Lagrangian or they do not even have an action at all?

score 2 · Accepted Answer · answered Apr 12 '20 at 16:05

That a set of equations does not have a variational formulation means that there does not exist an action functional, cf. e.g. this Phys.SE post.
The existence of a local functional is typically a separate issue, which is usually required in fundamental physics.

QFTs without Lagrangian

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