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--- formulas:canonical_commutation_relations [2018/05/03 13:41]
jakobadmin [Abstract]
+++ formulas:canonical_commutation_relations [2018/05/05 12:22]
138.186.136.73 ↷ Links adapted because of a move operation
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 \begin{equation} \label{qftcomm}  [\Phi(x), \pi(y)]=\Phi(x) \pi(y) - \pi(y) \Phi(x) = i \delta(x-y) \end{equation} where $\delta(x-y)$ is the Dirac delta distribution and $\pi(y) = \frac{\partial \mathscr{L}}{\partial(\partial_0\Phi)}$ is the conjugate momentum.
-It tells us that the fields in [[theories:quantum_field_theory|quantum field theory]] $\Phi(x)$ can‘t be simply a function, but must be __operators__. In contrast, ordinary functions and numbers commute:
+It tells us that the fields in [[theories:quantum_field_theory:canonical|quantum field theory]] $\Phi(x)$ can‘t be simply a function, but must be __operators__. In contrast, ordinary functions and numbers commute:
 For example $f(x)=3x$ and $g(y)= 7y^2 +3$ clearly commute $$ [f(x) , g(x)]= f(x)g(x) - g(x) f(x) = 3x (7y^2 +3) -(7y^2 +3) 3x =0. $$
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 The problem of finding an appropriate mathematical interpretation of the canonical commutation
 relations is the subject of [[advanced_tools:quantization|quantization theory]].
+----
+  * A good discussion can be found [[https://mathoverflow.net/questions/55988/quantum-mechanics-formalism-and-c-algebras/56003|here]].
 <tabbox Why is it interesting?>