How does the Stress Energy tensor relate to Noether's theorem?

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SUMMARY

The stress-energy tensor is fundamentally linked to Noether's theorem, arising naturally in special relativity through the framework of Lagrangians. It serves as a Noether current, representing conserved quantities associated with symmetries in physical systems. The discussion highlights the derivation of the stress-energy tensor from the Noether current, emphasizing its application in fields such as fluid dynamics, particularly in the context of "spacetime as a perfect fluid." David Tong's resource on quantum field theory provides a valuable reference for understanding these concepts.

PREREQUISITES
  • Understanding of Noether's theorem and its implications in physics
  • Familiarity with Lagrangian mechanics
  • Basic knowledge of special relativity
  • Introduction to differential forms (optional for deeper understanding)
NEXT STEPS
  • Study the derivation of the stress-energy tensor from Noether's theorem in detail
  • Explore David Tong's quantum field theory notes, specifically section 1.3.2
  • Research the application of the stress-energy tensor in fluid dynamics
  • Investigate the concept of "spacetime as a perfect fluid" and its implications in theoretical physics
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Physicists, students of theoretical physics, and researchers interested in the applications of Noether's theorem and the stress-energy tensor in various fields, including quantum field theory and general relativity.

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Hi,

I was wondering if the stress-energy tensor arose naturally in special relativity in the same way that plain energy and momentum do via Lagrangians. I understand Noether's theorem for particles, but Wikipedia describes the stress-energy tensor as a Noether current; can anyone explain what this is?
Unfortunately, I don't know enough about differential forms to follow the standard definition. The other derivations based on dust etc. all seem a little contrived, deriving vanishing divergence almost as an aftherthought. I'm hoping that this line of inquiry will bring me more satisfaction.

Thanks a lot!
 
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That's exactly what I need!
Thanks again
 
Sorry to bother again...I now understand the derivation of the Noether current, but which field do I apply it to if I want the standard stress-energy tensor? Is this where "spacetime as a perfect fluid" comes into play?
 

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