advanced_tools:gauge_symmetry:gauge_fixing
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
advanced_tools:gauge_symmetry:gauge_fixing [2017/11/05 15:34] jakobadmin ↷ Links adapted because of a move operation |
advanced_tools:gauge_symmetry:gauge_fixing [2018/04/03 17:54] (current) jakobadmin [Researcher] |
||
|---|---|---|---|
| Line 41: | Line 41: | ||
| Different gauges lead to different interpretations of the theory: | Different gauges lead to different interpretations of the theory: | ||
| - | * For example, when considering the [[theories:quantum_theory:quantum_field_theory:qcd_vacuum|QCD vacuum]] one usually uses the temporal gauge. This gauge makes it possible to derive the usual periodic picture of the QCD vacuum. This picture is convenient, because it allows us to understand quite pictorial what instantons are, namely tunneling processes between the vacua. However, in a different gauge like the axial gauge this picture does not emerge and there is just one non-degenerate vacuum (See section 10.3 in the book Classical Solutions in Quantum Field Theory by Erick Weinberg and [[https://journals.aps.org/prd/abstract/10.1103/PhysRevD.15.3656|Interpretation of pseudoparticles in physical gauges]] by Claude W. Bernard and Erick J. Weinberg. A remark in this later paper is [[https://inspirehep.net/record/1469386/files/A1991FE77000001.pdf|what gave Frank Wilczek the idea for the axion mechanism]].) Moreover, in the Coulomb gauge the situation is even different. There, one encounters the famous [[advanced_notions:quantum_field_theory:gribov_ambiguities|Gribov ambiguities]]. When one tries to fix the Coulomb gauge, one notices that this is not globally possible. Instead, at some points several gauge potentials get "picked out" by the gauge condition. The $\theta$ parameter appears as a relative phase between two ambiguous gauge potentials. In addition, in the Coulomb gauge there is only one vacuum. (See: [[https://journals.aps.org/prd/pdf/10.1103/PhysRevD.17.1576|Coulomb gauge description of large Yang-Mills fields]] by R. Jackiw et. al.) | + | * For example, when considering the [[advanced_notions:quantum_field_theory:qcd_vacuum|QCD vacuum]] one usually uses the temporal gauge. This gauge makes it possible to derive the usual periodic picture of the QCD vacuum. This picture is convenient, because it allows us to understand quite pictorial what instantons are, namely tunneling processes between the vacua. However, in a different gauge like the axial gauge this picture does not emerge and there is just one non-degenerate vacuum (See section 10.3 in the book Classical Solutions in Quantum Field Theory by Erick Weinberg and [[https://journals.aps.org/prd/abstract/10.1103/PhysRevD.15.3656|Interpretation of pseudoparticles in physical gauges]] by Claude W. Bernard and Erick J. Weinberg. A remark in this later paper is [[https://inspirehep.net/record/1469386/files/A1991FE77000001.pdf|what gave Frank Wilczek the idea for the axion mechanism]].) Moreover, in the Coulomb gauge the situation is even different. There, one encounters the famous [[advanced_notions:quantum_field_theory:gribov_ambiguities|Gribov ambiguities]]. When one tries to fix the Coulomb gauge, one notices that this is not globally possible. Instead, at some points several gauge potentials get "picked out" by the gauge condition. The $\theta$ parameter appears as a relative phase between two ambiguous gauge potentials. In addition, in the Coulomb gauge there is only one vacuum. (See: [[https://journals.aps.org/prd/pdf/10.1103/PhysRevD.17.1576|Coulomb gauge description of large Yang-Mills fields]] by R. Jackiw et. al.) |
| * Another example is the Higgs mechanism. In the usually used unitary gauge, we get the now famous picture with the "Mexican Hat Potential" and the marble that runs down from the top to the new minimum, which corresponds to a non-zero vacuum expectation value of the Higgs field. However, in the temporal gauge this picture does not emerge. In this gauge the vacuum expectation value of the Higgs field is zero. (See [[https://inspirehep.net/record/6474|Higgs Mechanism in the Temporal Gauge]] by Michael Creutz, Thomas N. Tudron and [[http://www.sciencedirect.com/science/article/pii/055032138190448X|Higgs phenomenon without symmetry breaking order parameter]] by J. Fröhlich et. al.) | * Another example is the Higgs mechanism. In the usually used unitary gauge, we get the now famous picture with the "Mexican Hat Potential" and the marble that runs down from the top to the new minimum, which corresponds to a non-zero vacuum expectation value of the Higgs field. However, in the temporal gauge this picture does not emerge. In this gauge the vacuum expectation value of the Higgs field is zero. (See [[https://inspirehep.net/record/6474|Higgs Mechanism in the Temporal Gauge]] by Michael Creutz, Thomas N. Tudron and [[http://www.sciencedirect.com/science/article/pii/055032138190448X|Higgs phenomenon without symmetry breaking order parameter]] by J. Fröhlich et. al.) | ||
| Line 48: | Line 48: | ||
| - | --> Common Question 1# | ||
| - | |||
| - | <-- | ||
| - | |||
| - | --> Common Question 2# | ||
| - | |||
| - | |||
| - | <-- | ||
| - | | ||
| <tabbox Examples> | <tabbox Examples> | ||
advanced_tools/gauge_symmetry/gauge_fixing.1509892488.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
