I've read here that it's not possible to construct a field theory which is invariant under boosts but not invariant under rotations. The reason is essentially that boosts aren't closed under composition, i.e. they don't form a group. Now the Lorentz group, which includes rotations and boosts, is obviously a group, and it does not include translations (in spacetime). Now I wonder if it is possible to construct a field theory which is invariant under the Lorentz group but not invariant under translations. Are there any physically interesting examples of this?
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