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 advanced_notions:quantum_field_theory:instantons [2018/04/09 10:59]tesmitekle advanced_notions:quantum_field_theory:instantons [2018/05/05 11:52] (current)jakobadmin ↷ Links adapted because of a move operation Both sides previous revision Previous revision 2018/05/05 11:52 jakobadmin ↷ Links adapted because of a move operation2018/04/09 10:59 tesmitekle 2018/03/24 14:48 ↷ Links adapted because of a move operation2018/03/17 15:59 jakobadmin [Student] 2018/03/17 15:54 jakobadmin [Student] 2018/03/17 15:52 jakobadmin [Student] 2018/03/17 15:51 jakobadmin [Layman] 2018/03/17 15:49 jakobadmin [Student] 2018/03/17 15:48 jakobadmin [Student] 2018/03/17 15:47 jakobadmin [Student] 2018/03/17 15:40 jakobadmin [Student] 2018/03/17 15:40 jakobadmin [Researcher] 2018/03/17 15:39 jakobadmin [Researcher] 2018/03/17 15:39 jakobadmin [Student] 2018/03/17 15:38 jakobadmin [Student] 2018/03/17 15:38 jakobadmin [Student] 2018/03/17 15:36 jakobadmin [Student] 2018/03/17 15:36 jakobadmin [Student] 2018/03/17 15:35 jakobadmin [Student] 2018/03/17 15:34 jakobadmin [Student] 2018/03/12 17:15 jakobadmin [Why is it interesting?] 2018/03/12 16:51 jakobadmin [Student] 2017/12/04 08:01 external edit2017/11/17 14:36 jakobadmin [Student] 2017/11/17 14:35 jakobadmin [Student] 2017/11/15 09:48 jakobadmin 2017/11/08 16:48 jakobadmin [Researcher] 2018/05/05 11:52 jakobadmin ↷ Links adapted because of a move operation2018/04/09 10:59 tesmitekle 2018/03/24 14:48 ↷ Links adapted because of a move operation2018/03/17 15:59 jakobadmin [Student] 2018/03/17 15:54 jakobadmin [Student] 2018/03/17 15:52 jakobadmin [Student] 2018/03/17 15:51 jakobadmin [Layman] 2018/03/17 15:49 jakobadmin [Student] 2018/03/17 15:48 jakobadmin [Student] 2018/03/17 15:47 jakobadmin [Student] 2018/03/17 15:40 jakobadmin [Student] 2018/03/17 15:40 jakobadmin [Researcher] 2018/03/17 15:39 jakobadmin [Researcher] 2018/03/17 15:39 jakobadmin [Student] 2018/03/17 15:38 jakobadmin [Student] 2018/03/17 15:38 jakobadmin [Student] 2018/03/17 15:36 jakobadmin [Student] 2018/03/17 15:36 jakobadmin [Student] 2018/03/17 15:35 jakobadmin [Student] 2018/03/17 15:34 jakobadmin [Student] 2018/03/12 17:15 jakobadmin [Why is it interesting?] 2018/03/12 16:51 jakobadmin [Student] 2017/12/04 08:01 external edit2017/11/17 14:36 jakobadmin [Student] 2017/11/17 14:35 jakobadmin [Student] 2017/11/15 09:48 jakobadmin 2017/11/08 16:48 jakobadmin [Researcher] 2017/11/08 16:39 jakobadmin [Researcher] 2017/11/08 16:37 jakobadmin created Line 15: Line 15: Such processes cannot be described by [[advanced_notions:​quantum_field_theory:​perturbation_theory|perturbation theory]], but instead only with the help of [[advanced_tools:​non-perturbative_qft|non-perturbative methods]]. This follows since the wave function of tunnel processes is proportional to $e^{1/x}$ or $e^{1/x^2}$ and the Taylor expansion of such functions vanishes. Hence such effects do not appear in a perturbative expansion also, of course, these effects exist. Such processes cannot be described by [[advanced_notions:​quantum_field_theory:​perturbation_theory|perturbation theory]], but instead only with the help of [[advanced_tools:​non-perturbative_qft|non-perturbative methods]]. This follows since the wave function of tunnel processes is proportional to $e^{1/x}$ or $e^{1/x^2}$ and the Taylor expansion of such functions vanishes. Hence such effects do not appear in a perturbative expansion also, of course, these effects exist. - The [[advanced_notions:​quantum_field_theory:​qcd_vacuum|ground state]] of, for example, [[models:​qcd|QCD]] consists of an infinite number of degenerate states that are separated by a finite energy barrier. An instanton is a description how the field tunnels (not meant in a spatial sense) through one of these barriers into another vacuum. During the tunnel process the field, also in the ground state at the beginning and end of the process, goes continuously through a set of field configurations that do not correspond to a ground state, i.e. non-zero field energy. This is meant when we say that an instanton "​has"​ finite field energy. + The [[advanced_notions:​quantum_field_theory:​qcd_vacuum|ground state]] of, for example, [[models:​standard_model:qcd|QCD]] consists of an infinite number of degenerate states that are separated by a finite energy barrier. An instanton is a description how the field tunnels (not meant in a spatial sense) through one of these barriers into another vacuum. During the tunnel process the field, also in the ground state at the beginning and end of the process, goes continuously through a set of field configurations that do not correspond to a ground state, i.e. non-zero field energy. This is meant when we say that an instanton "​has"​ finite field energy. A detailed discussion of instantons written with the needs of students in mind can be found [[http://​jakobschwichtenberg.com/​demystifying-the-qcd-vacuum-part-1/​|here]]. ​ A detailed discussion of instantons written with the needs of students in mind can be found [[http://​jakobschwichtenberg.com/​demystifying-the-qcd-vacuum-part-1/​|here]]. ​