- #1
bagherihan
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Is there anywhere I can see the explicit derivation for a massless real scalar and for the EM field?
thank you.
thank you.
ChrisVer said:What do you actually mean?
You can always try to find the Noether current for Lorentz transformations in both cases...The result current I think is the Energy Momentum tensor...
bagherihan said:I mean for example that I saw that for the scalar field it is :
[tex]
j^{μσμ} = x^ρT^{\mu \sigma} - x^σT^{\mu ρ}
[/tex]
I don't know how to get there, so I'd like to see the full derivation.
The Noether currents under Lorentz Transformation are significant because they represent the conservation laws of energy, momentum, and angular momentum in special relativity. These currents provide a way to mathematically describe the transformation properties of physical quantities under Lorentz transformations, which are crucial for understanding the symmetries of the laws of physics.
The derivation of Noether currents under Lorentz Transformation involves using the Noether theorem, which states that for every continuous symmetry in a physical system, there exists a conserved quantity. In this case, the symmetry is the invariance of the laws of physics under Lorentz transformations. By applying the theorem to the Lagrangian of the system, we can obtain the Noether currents.
Tensors play a crucial role in the derivation of Noether currents under Lorentz Transformation, as they are used to represent the transformation properties of physical quantities. In special relativity, tensors are used to describe how physical quantities, such as energy and momentum, change under Lorentz transformations. By using tensors, we can obtain the Noether currents in a covariant and consistent manner.
Yes, Noether currents can be derived for any physical system that exhibits symmetry under Lorentz transformations. This includes classical mechanics, electromagnetism, and quantum field theory. However, the specific form of the Noether currents may vary depending on the system and the symmetries present.
The Noether currents under Lorentz Transformation have many implications for modern physics, particularly in the fields of special relativity and quantum field theory. These currents provide a deep understanding of the symmetries of physical laws and allow us to make predictions about the behavior of physical systems. They also have applications in particle physics, where they are used to study the conservation of energy and momentum in subatomic interactions.