advanced_notions:quantum_field_theory:gribov_ambiguities
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advanced_notions:quantum_field_theory:gribov_ambiguities [2017/05/14 11:10] jakobadmin |
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 ====== | ||
| - | It was proven by Singer in "Some Remarks on the Gribov Ambiguity" that "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. " | + | |
| <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. | ||
| + | |||
| + | |||
| + | <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> | ||
advanced_notions/quantum_field_theory/gribov_ambiguities.1494753042.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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