I Momentum cutoff, Lorentz violation and the vacuum state

[asimov42]

Hi all - related to a question I asked some time ago: If one introduces a momentum cutoff, the result in the most basic case is Lorentz violation. That is, some form of preferred frame must be introduced. I'm wondering what this does to the vacuum state? That is, how does one keep the vacuum 'empty' despite this preferred frame? Or does the notion of the vacuum have to change?

 

[asimov42]

By 'empty' I mean that the vacuum can only be in the ground state in the preferred frame, correct?

 

[Demystifier]

By 'empty' I mean that the vacuum can only be in the ground state in the preferred frame, correct?

Correct. But if Lorentz symmetry is no longer the symmetry of the theory, then it is pretty much pointlesss to even ask how the vacuum (or anything else) looks in other Lorentz frames.

 

[asimov42]

Thanks @Demystifier. If one were to do the totally naive thing and introduce a momentum cutoff in the preferred frame, without changing other aspects of the theory, what would one expect to observe?

 

[Demystifier]

Thanks @Demystifier. If one were to do the totally naive thing and introduce a momentum cutoff in the preferred frame, without changing other aspects of the theory, what would one expect to observe?

An ugly but consistent theory that can be compared with experiments.

 

[asimov42]

Certainly - but then there should be an expected (predicted) observation. For example, applying a boost in the 'right' direction should make the ground state in the preferred frame look excited in another, no?

 

[Keith_McClary]

make the ground state in the preferred frame look excited in another

Yes. I would call it a computational approximation rather than a "theory". Like ignoring the curvature of the Earth in a ballistic calculation.

 

[Demystifier]

Certainly - but then there should be an expected (predicted) observation. For example, applying a boost in the 'right' direction should make the ground state in the preferred frame look excited in another, no?

I think it depends on how exactly do you compute the boost, i.e. what do you keep fixed. Have you tried to do the actual calculation? For free fields it should not be difficult.