Problem: Prove invariance of momentum factor

In summary, the conversation discusses the derivation of scattering amplitudes and questions how to prove the Lorentz invariance of the momentum uncertainty element. It is suggested that the proof is similar to that of the measure d^3p/E, which relies on the properties of the dirac delta function. However, it is unclear how this would apply to uncertainties.
  • #1
popffabrik1
5
0
Hi,

In the derivation of scattering amplitudes (e.g. page 94 in http://kcl.ac.uk/content/1/c6/06/20/94/LecturesSM2010.pdf ) does anyone have a clue as to how to prove that the momentum uncertainty element

(\delta p)^3/E

is Lorentz invariant? I know how to do it for the measure d^3p/E, but I am not sure how to proceed for the given (non-infinitesimal) element.

Thank,

P
 
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  • #2
I would say that it is proven in the same was as for the measure.
 
  • #3
For the measure, you prove it by noting that
\int d^4p \delta(p^2)
is a lorentz invariant and by the properties of the dirac delta function this reduces to the given measure over three momentum. I don't see how there would be an analog in the case of 'errors'
 

Related to Problem: Prove invariance of momentum factor

What is the definition of momentum factor?

Momentum factor is a physical quantity that describes the amount of motion an object has based on its mass and velocity. It is calculated by multiplying an object's mass by its velocity.

Why is it important to prove the invariance of momentum factor?

Proving the invariance of momentum factor is important because it is a fundamental principle in physics and is used to understand and predict the behavior of objects in motion. It also helps to validate the laws of conservation of momentum.

What evidence is needed to prove the invariance of momentum factor?

To prove the invariance of momentum factor, we need to gather experimental data that shows that the momentum factor remains constant in different reference frames. This can be done through controlled experiments and mathematical calculations.

How does the invariance of momentum factor relate to Newton's laws of motion?

The invariance of momentum factor is closely related to Newton's laws of motion, particularly the law of inertia. This law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The invariance of momentum factor supports this law by showing that the momentum of an object remains constant unless acted upon by an external force.

Are there any exceptions to the invariance of momentum factor?

Yes, there are exceptions to the invariance of momentum factor, such as when an external force is applied to an object, causing its momentum to change. Additionally, the invariance of momentum factor does not hold in the field of quantum mechanics, where the concept of momentum is more complex.

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