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

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In summary, Emmy Noether's theorems state that for every differentiable continuous symmetry, there is a correlated conservation. While the classical formulation of these theorems is simple, the field theory formulation can be more complex. To gain a deeper understanding of Noether's theorems in field theory, you can refer to notes and books such as "Symmetries in Quantum Field Theory" by S. Weinberg. This book covers symmetry principles extensively and is highly recommended. Additionally, Noether's theorems only apply to continuous symmetries, not discontinuous ones like parity.
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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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  • #2
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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FAQ: Understand Emmy Noether's Theorems for Field Theory & Discontinuous Symmetries

1) What is Emmy Noether's Theorem for Field Theory?

Emmy Noether's Theorem for Field Theory is a mathematical theorem that relates the symmetries of a physical system to the conservation laws that govern it. It states that for every continuous symmetry of a physical system, there exists a corresponding conserved quantity.

2) What are discontinuous symmetries in the context of Emmy Noether's Theorem?

Discontinuous symmetries are transformations that do not smoothly and continuously transform a physical system, but instead have abrupt changes. These symmetries are important in Emmy Noether's Theorem because they can still result in conserved quantities, but the relationship is more complex than for continuous symmetries.

3) How does Emmy Noether's Theorem apply to field theory?

In the context of field theory, Emmy Noether's Theorem states that for every continuous symmetry of a field, there exists a corresponding conserved current. This means that if the equations of motion for a field are invariant under a certain transformation, there is a corresponding physical quantity that remains constant throughout the system's evolution.

4) How does Emmy Noether's Theorem relate to the laws of physics?

Emmy Noether's Theorem is important in physics because it provides a deep mathematical connection between symmetries and the fundamental laws that govern physical systems. It shows that symmetries play a crucial role in understanding the behavior of physical systems and can reveal underlying principles and conservation laws.

5) What are some real-world applications of Emmy Noether's Theorem?

Emmy Noether's Theorem has been applied in various areas of physics, including classical mechanics, quantum mechanics, and general relativity. It has also been used in the study of particle physics, condensed matter physics, and cosmology. It has helped to uncover new conservation laws and deepen our understanding of the fundamental laws of nature.

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