# Momentum cutoff, Lorentz violation and the vacuum state

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• asimov42
In summary: I think it depends on how exactly do you compute the boost, i.e. what do you keep fixed.I haven't tried to do the calculation, but I think it would be a pretty straightforward exercise. You just keep the energy and momentum of the particles in the system fixed.I haven't tried to do the calculation, but I think it would be a pretty straightforward exercise.
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?

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

asimov42 said:
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.

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?

asimov42 said:
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.

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?

asimov42 said:
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.

asimov42 said:
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.

## 1. What is momentum cutoff?

Momentum cutoff is a theoretical concept used in physics to describe the maximum momentum that a particle can have. This is often used in calculations involving quantum field theory and is related to the idea of a "cutoff scale" in which high energy interactions are suppressed.

## 2. How does Lorentz violation affect momentum cutoff?

Lorentz violation refers to a theoretical violation of the Lorentz invariance, which is a fundamental symmetry in the laws of physics. This can affect the concept of momentum cutoff by introducing new terms and interactions that may alter the behavior of particles at high energies.

## 3. What is the significance of Lorentz violation in the vacuum state?

Lorentz violation in the vacuum state is of great interest in theoretical physics as it could potentially lead to new insights into the nature of spacetime and the fundamental laws of the universe. It is also relevant in the study of quantum gravity and the search for a unified theory of physics.

## 4. How is the vacuum state affected by momentum cutoff?

The vacuum state, also known as the ground state, is the lowest energy state of a quantum system. Momentum cutoff can affect the vacuum state by introducing new energy scales and interactions that may change the properties of the vacuum and the behavior of particles in it.

## 5. Is there any experimental evidence for Lorentz violation or momentum cutoff?

There have been several experiments conducted to search for evidence of Lorentz violation and momentum cutoff, but so far, no conclusive results have been found. This is an active area of research, and further experiments and theoretical developments are needed to fully understand these concepts and their implications.

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