====== Cocycles ======

<tabbox Why is it interesting?> 

"In field theory and in modern elementary particle theory, cocycles
are used to describe [[advanced_notions:quantum_field_theory:anomalies|anomalies]]." ([[https://inspirehep.net/record/213998/files/v15-n3-p99.pdf|Source]])

1-cocycles are used to understand anomalies in the Lagrangian framework. The 1-cocycles show up in the non-conservation of classically conserved currents. 

2-cocycles are used to understand anomalies in the Hamiltonian framework. They have the effect that it becomes impossible to satisfy Gauss' law.
([[https://inspirehep.net/record/213998/files/v15-n3-p99.pdf|Source]])
<tabbox Layman> 

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student> 
For a great introduction see https://inspirehep.net/record/213998/files/v15-n3-p99.pdf and chapter III in Analysis On Infinite Dimensional Manifolds: Schrodinger Representation For Quantized Fields by R. Jackiw
<tabbox Researcher> 

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

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<tabbox Examples> 

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<tabbox History> 

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