Four momentum vector from energy-momentum-tensor

In summary, the four momentum vector is a mathematical quantity used in physics to describe the motion and energy of particles. It is related to the energy-momentum tensor through the conservation of energy and momentum and can be calculated using Lorentz transformation equations. It is only applicable to particles that follow the laws of special relativity and changes in different reference frames due to time dilation and length contraction. The four momentum vector has important physical implications, including its role in the conservation of energy and momentum and its use in calculations of particle mass and energy.
  • #1
torus
21
0
Hi,
for a real scalar field one has the energy momentum tensor from Noethers theorem
[tex]T^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial \partial_\mu \phi} \partial^\nu \phi - \eta^{\mu\nu} \mathcal{L} [/tex]
and the conserved quantities
[tex]P^\nu = \int d^3 x \ T^{0\nu}[/tex]

Now, how can one show that P is really a 4-vector, since the definition looks not that covariant and I could not think of anything.

Thanks for your response,
torus
 
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  • #3
Ah, thanks a lot.
 

FAQ: Four momentum vector from energy-momentum-tensor

1. What is the four momentum vector and how is it related to the energy-momentum tensor?

The four momentum vector is a mathematical quantity used in the field of physics to describe the motion and energy of particles. It is related to the energy-momentum tensor through the conservation of energy and momentum, as the components of the four momentum vector correspond to the energy and momentum in different directions.

2. How is the four momentum vector calculated from the energy-momentum tensor?

The four momentum vector can be calculated from the energy-momentum tensor by using the Lorentz transformation equations. These equations take into account the effects of relativistic motion and allow for the calculation of the four momentum vector from the components of the energy-momentum tensor.

3. Can the four momentum vector be used to describe the motion of all particles?

No, the four momentum vector is only applicable to particles that follow the laws of special relativity. This includes particles with mass, such as protons and electrons, but does not apply to massless particles such as photons.

4. How does the four momentum vector change in different reference frames?

The four momentum vector is a relativistic quantity, meaning it changes in different reference frames. This is due to the effects of time dilation and length contraction, which affect the components of the vector and cause it to change in different reference frames.

5. What are the physical implications of the four momentum vector?

The four momentum vector has important physical implications, as it is directly related to the conservation of energy and momentum in particle interactions. It is also used in calculations of particle mass and energy, as well as in the understanding of relativistic motion and the behavior of particles at high speeds.

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