Is Poincare symmetry the real thing?

[Ilja]

There are many actions invariant under the group of the lattice but not under the rotation group. All these must be excluded by fine-tuning. There is no renormalization criterion that would exclude the rotation symmetry-violating higher order terms of the action.

Why do you think so? The straightforward continuous limit is nothing else but what renormalization gives. Of course, with postulating some symmetries one can restrict the terms which are allowed in a renormalization procedure. But this does not give the other terms greater long distance effects. They may disappear in the long distance limit as well. What survives at long distances are only the lowest order terms.

 

[Ilja]

But isn't a similar feature present in standard field theories? Even though the equations of motion are dynamical, one puts restrictions on initial conditions, e.g. that the field must vanish at infinity. What's the difference between such standard restrictions and your restrictions?

Why do you ask me?

I think that your claim that there is a certain distinction between fixed and dynamical degrees of freedom has a problem with the preferred coordinates - the straightforward example of something fixed, as describing absolute space and time - fulfilling a quite dynamical-looking equation.

It was an aspect of my claim that covariance is nothing physical, given that every classical theory allows a covariant formulation.

If one, anyway, has to add some fixed boundary conditions even for really dynamical entities, your problem to distinguish them becomes even greater.