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advanced_tools:connections [2018/04/14 13:38] theodorekorovin |
advanced_tools:connections [2018/05/06 13:33] jakobadmin [Concrete] |
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====== Connections ====== | ====== Connections ====== | ||
- | //also known as a path lifting rule in the context of [[advanced_tools:fiber_bundles|fiber bundles]] and as gauge fields on particle physics // | + | //also known as a path lifting rules in the context of [[advanced_tools:fiber_bundles|fiber bundles]] and as gauge fields in particle physics // |
<tabbox Intuitive> | <tabbox Intuitive> | ||
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<tabbox Concrete> | <tabbox Concrete> | ||
+ | [[{{ :advanced_tools:gaugeconnection.png?nolink |Source: https://theorie.ikp.physik.tu-darmstadt.de/qcd/moore/latt_lectures.pdf}}]] | ||
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The two most important types of connections are | The two most important types of connections are | ||
* The [[advanced_tools:connections:ehresmann_connection]], which is appropriate tool to describe parallel transport in gauge theories. The parallel transport here happens on the fiber bundle, i.e. from one fiber to the next. Each fiber is one copy of our gauge group, e.g. $U(1)$. Our gauge fields, like the electromagnetic field is described by an Ehresmann connection. | * The [[advanced_tools:connections:ehresmann_connection]], which is appropriate tool to describe parallel transport in gauge theories. The parallel transport here happens on the fiber bundle, i.e. from one fiber to the next. Each fiber is one copy of our gauge group, e.g. $U(1)$. Our gauge fields, like the electromagnetic field is described by an Ehresmann connection. | ||
- | * The [[advanced_tools:connections:levi_civita_connection]], which is the appropriate tool to describe parallel transport in [[models:general_relativity|General Relativity]]. The gravitational field is described by a Levi-Civita connection | + | * The [[advanced_tools:connections:levi_civita_connection]], which is the appropriate tool to describe parallel transport in [[theories:general_relativity|General Relativity]]. The gravitational field is described by a Levi-Civita connection |
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