advanced_notions:quantum_field_theory:ghosts

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advanced_notions:quantum_field_theory:ghosts [2018/03/30 10:57] jakobadmin [Concrete] |
advanced_notions:quantum_field_theory:ghosts [2018/03/30 10:57] (current) jakobadmin [Abstract] |
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+ | The group of [[advanced_tools:gauge_symmetry|gauge transformations]] $G$ means the bundles automorphisms which preserve the Lagrangian. ([[http://www.mathunion.org/ICM/ICM1978.2/Main/icm1978.2.0881.0886.ocr.pdf|Source]]) | ||

- | | + | The gauge group is simply one fiber of the bundle, i.e. for example, $SU(2)$. |

- | | + | |

- | The group of gauge transformations $G$ means the bundles automorphisms which preserve the Lagrangian. ([[http://www.mathunion.org/ICM/ICM1978.2/Main/icm1978.2.0881.0886.ocr.pdf|Source]]) | + | |

- | | + | |

- | The gauge group is simply one fibre of the bundle, i.e. for example, $SU(2)$. | + | |

We denote the space of all connections by $A$. Now, to get physically sensible results we must be careful with these different notions: | We denote the space of all connections by $A$. Now, to get physically sensible results we must be careful with these different notions: | ||

<blockquote> | <blockquote> | ||

- | Integration should therefore be carried out on the quotient space $\mathcal{G}=A/G$. Now $A$ is a linear space but $\mathcal{G}$ is only a manifold and has to be treated with more respect. Thus for integration purposes a Jacobian term arises which, in perturbation theory, gives rise to the well-known Faddeev-Popov "ghost" particles. Nonperturbatively it seems reasonable that global topological features of $\mathcal{G}$ will be relevant. | + | Integration should, therefore, be carried out on the quotient space $\mathcal{G}=A/G$. Now $A$ is a linear space but $\mathcal{G}$ is only a manifold and has to be treated with more respect. Thus for integration purposes a Jacobian term arises which, in perturbation theory, gives rise to the well-known Faddeev-Popov "ghost" particles. Nonperturbatively it seems reasonable that global topological features of $\mathcal{G}$ will be relevant. |

<cite>Geometrical Aspects of Gauge Theories by M. F. Atiyah</cite> | <cite>Geometrical Aspects of Gauge Theories by M. F. Atiyah</cite> |

advanced_notions/quantum_field_theory/ghosts.txt · Last modified: 2018/03/30 10:57 by jakobadmin

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