Understand Emmy Noether's Theorems for Field Theory & Discontinuous Symmetries

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SUMMARY

Emmy Noether's theorems establish a fundamental relationship between continuous symmetries and conservation laws in physics. The classical formulation is straightforward, but the field theory formulation presents complexities that require deeper understanding. For comprehensive insights into Noether's theorems in the context of field theory, S. Weinberg's "Quantum Theory of Fields" (Cambridge University Press, 3 Vols.) is highly recommended. Additionally, the discussion highlights the limitation of Noether's theorems to continuous symmetries, raising questions about the treatment of discontinuous symmetries such as parity.

PREREQUISITES
  • Understanding of continuous and discontinuous symmetries in physics
  • Familiarity with classical mechanics and conservation laws
  • Knowledge of quantum field theory (QFT)
  • Experience with electrodynamics and quantum mechanics
NEXT STEPS
  • Study the detailed formulations of Noether's theorems in S. Weinberg's "Quantum Theory of Fields"
  • Research the implications of discontinuous symmetries in quantum field theory
  • Examine the role of symmetries in conservation laws across different physical theories
  • Explore lecture notes on symmetries in quantum field theory available at the provided link
USEFUL FOR

Physicists, graduate students in theoretical physics, and anyone interested in the advanced applications of Noether's theorems in field theory and symmetry analysis.

akai_ma
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ok so I understand the general idea of Emmy Noether's theorems, for every differentiable continuous symmetry there is a correlated conservation. The classical formulation seems simple enough, but the field theory formulation seems nasty. I have been through electrodynamics and quantum mechanics. So my question is this:
Where can I find an in depth understadable formulation of Noether's theorems for field theory?
Also from what I've read the theorems only work for continuous symmetries. What about discontinuous symmetries like parity?
 
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You find some discussion on symmetries in quantum field theory in my notes,

http://theorie.physik.uni-giessen.de/~hees/publ/lect.pdf

The (in my opinion) best qft books are

S. Weinberg, Quantum Theory of Fields, Cambride University Press (3 Vols.)

They cover symmetry principles very thoroughly.
 
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