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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]
jakobadmin [Abstract]
@@ Line 33: / Line 33: @@
 <tabbox Abstract>
+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:
 <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>

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