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advanced_notions:observable [2017/12/04 09:01]
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advanced_notions:observable [2018/01/02 13:13]
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-====== Observable ====== 
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-<tabbox Why is it interesting?> ​ 
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-<tabbox Layman> ​ 
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-<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>​ 
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-<tabbox Student> ​ 
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-<note tip> 
-In this section things should be explained by analogy and with pictures and, if necessary, some formulas. 
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-<tabbox Researcher> ​ 
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-In the path integral approach to gauge theory, observables are gauge invariant functions on the space $\mathcal A$ of a $G$-connections on $E$, where $G$ denotes the structure group and $E$ the fiber bundle. Therefore, an observable $f$ is a function on the space $\mathcal A / \mathcal G$, of connections modulo gauge transformations. 
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-As a result, vacuum expectation values are no longer defined as integrals with Lebesgue measure $ \mathcal A$, but instead with a Lebesgue measure on $ \mathcal A/ \mathcal G$. We obtain this measure by pushing forward the Lebesgue measure on $ \mathcal A$ by the map  $ \mathcal A \to \mathcal A/ \mathcal G$ that sends each connection to its gauge equivalence class, and then $ A$ denotes a gauge equivalence class of connections in the integral. 
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-The simplest example of an observable in gauge theory are Wilson loops. ​ 
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-Take note that this procedure of modding out $\mathcal G$ from $\mathcal A$ is what leads to [[theories:​quantum_theory:​quantum_field_theory:​ghosts|Ghosts]]. To do this properly requires to make use of the [[advanced_tools:​gauge_symmetry:​brst|BRST]] formalism. ​ 
-(Source: Baez, Munian; Gauge Fields, Knots and Gravity, page 342) 
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-<tabbox Examples> ​ 
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---> Example1# 
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-<-- 
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---> Example2:# 
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-<-- 
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-<tabbox FAQ> ​ 
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-<tabbox History> ​ 
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-</​tabbox>​ 
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advanced_notions/observable.txt · Last modified: 2018/01/02 14:13 by jakobadmin