advanced_notions:quantum_field_theory:instantons
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advanced_notions:quantum_field_theory:instantons [2018/03/17 15:54] jakobadmin [Student] |
advanced_notions:quantum_field_theory:instantons [2018/03/17 15:59] jakobadmin [Student] |
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| The [[advanced_notions:quantum_field_theory:cd_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:cd_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. | ||
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| + | 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]]. | ||
| Instantons occur in pure Yang-Mills theory with a non-abelian gauge group, for example, $SU(2)$. In contrast to Dirac monopoles and 't Hooft-Polyakov monopoles, Instantons do care about time. That's where their name comes from: they are localized in space and time. Therefore, this time we must consider their behavior in space and time. For reasons explained [[advanced_tools:non-perturbative_qft|here]], we describe tunnel processes in Euclidean spacetime, instead of Minkowski spacetime. Thus, for instantons, we investigate their behavior in $\mathbb{R}^4$. | Instantons occur in pure Yang-Mills theory with a non-abelian gauge group, for example, $SU(2)$. In contrast to Dirac monopoles and 't Hooft-Polyakov monopoles, Instantons do care about time. That's where their name comes from: they are localized in space and time. Therefore, this time we must consider their behavior in space and time. For reasons explained [[advanced_tools:non-perturbative_qft|here]], we describe tunnel processes in Euclidean spacetime, instead of Minkowski spacetime. Thus, for instantons, we investigate their behavior in $\mathbb{R}^4$. | ||
advanced_notions/quantum_field_theory/instantons.txt · Last modified: 2021/10/01 11:46 by 79.35.127.248
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