nLab
field strength

Context

Physics

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Surveys, textbooks and lecture notes

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    • Axiomatizations

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Differential cohomology

Ingredients

Connections on bundles

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Higher abelian differential cohomology

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Higher nonabelian differential cohomology

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Fiber integration

Application to gauge theory

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Contents

Idea

In gauge theory cocycles in differential cohomology model gauge fields.

By definition, every differential cohomology theory Γ ()\Gamma^\bullet(-) comes with a characteristic curvature form morphism

F:Γ¯ (X)Ω (X)π *Γ, F : \bar \Gamma^\bullet(X) \to \Omega^\bullet(X)\otimes \pi_*\Gamma \otimes \mathbb{R} \,,

the (generalized) Chern character.

For cΓ (X)c \in \Gamma^\bullet(X) a cocycle representing a gauge field in gauge theory, its image F(c)Ω (X)F(c) \in \Omega^\bullet(X) is the field strength of the gauge field. If we think of this cocycle as being (a generalization of) a connection on a bundle, this is essentially the curvature of that connection.

Often gauge fields are named after their field strength. For instance the field strength of the electromagnetic field is the 22-form FΩ 2(X)F \in \Omega^2(X) whose components are the electric and the magnetic fields.

Examples

: models and components

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Last revised on January 7, 2013 at 21:53:42. See the history of this page for a list of all contributions to it.