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advanced_notions:quantum_field_theory:gribov_ambiguities [2017/05/13 10:41] jakobadmin [Why is it interesting?] |
advanced_notions:quantum_field_theory:gribov_ambiguities [2017/11/05 15:34] (current) jakobadmin ↷ Page moved from theories:gauge_theory:gribov_ambiguities to advanced_notions:quantum_field_theory:gribov_ambiguities |
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====== Gribov Ambiguities ====== | ====== Gribov Ambiguities ====== | ||
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<tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
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<tabbox Student> | <tabbox Student> | ||
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<blockquote> | <blockquote> | ||
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<tabbox Researcher> | <tabbox Researcher> | ||
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+ | <blockquote> | ||
+ | There is a difficulty which arises in the cornpactified | ||
+ | case which is not present in the more general one. This | ||
+ | involves gauge fixing and the Gribov ambiguity. ' As | ||
+ | yet the gauge has not been fixed and there is the possibility | ||
+ | that fixing the gauge could affect the topology of | ||
+ | configuration space. The object of gauge fixing is to | ||
+ | choose one member from each class of gauge-equivalent | ||
+ | configurations so that there will be no double counting | ||
+ | of configurations in the path integral. | ||
+ | In the fiber-bundle picture of Dowker, ' | ||
+ | this corresponds | ||
+ | to finding a section in the bundle, reducing each | ||
+ | configuration fiber to a particular configuration in the fiber. The difficulty is that Singer' has proven that | ||
+ | there are no global gauges when space is compactified to | ||
+ | S . That is, there is no global section of the fiber bundle | ||
+ | that Dowker is using. This means that the space of | ||
+ | gauge-fixed configurations is disconnected. The answer is that the Gribov ambiguity allows for | ||
+ | certain zero-action discontinuous evolutions. Because | ||
+ | there are no global sections, the gauge fixing fails to always | ||
+ | specify a unique configuration from each | ||
+ | configuration fiber. When it does fail, there are two (or | ||
+ | more) configurations which are related by a gauge transformation. | ||
+ | Each of these lies on a different section of | ||
+ | the fiber bundle and one's histories may move between | ||
+ | the disconnected sections by way of these configurations. | ||
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+ | <cite>Nontrivial homotopy and tunneling by topological instantons by Arlen Anderson</cite> | ||
+ | </blockquote> | ||
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+ | It was proven by Singer in "Some Remarks on the Gribov Ambiguity", provided that we compactify spacetime to the 4-sphere, that <q>"no continuous choice of exactly one | ||
+ | connection on each orbit can be made. Thus the Gribov ambiguity for the | ||
+ | Coloumb gauge will occur in all other gauges. No gauge fixing is possible. "</q> | ||
<blockquote> | <blockquote> |