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In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops. They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops. In pure gauge theory they play the ...
The fiber of over a point () consists of the pairs (,) where is a path from () = to , i.e. the loop space . The inclusion Ω B ↪ F i {\displaystyle \Omega B\hookrightarrow F_{i}} of the fiber of i {\displaystyle i} into the homotopy fiber of i {\displaystyle i} is again a homotopy equivalence and iteration yields the sequence:
Pullback bundle. In mathematics, a pullback bundle or induced bundle [1] [2] [3] is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and a continuous map f : B′ → B one can define a "pullback" of E by f as a bundle f*E over B′. The fiber of f*E over a point b′ in B′ is just the fiber of E ...
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Striatopallidal fibres. The striatopallidal fibres, also Wilson's pencils, [1] [2] pencil fibres of Wilson, [3] and pencils of Wilson, are prominent myelinated fibres that connect the striatum to the globus pallidus . Their distinctive appearance allows the putamen to be identified on light microscopy .
A G-bundle is a fiber bundle with an equivalence class of G-atlases. The group G is called the structure group of the bundle; the analogous term in physics is gauge group. In the smooth category, a G-bundle is a smooth fiber bundle where G is a Lie group and the corresponding action on F is smooth and the transition functions are all smooth maps.
Fiberscope. A low quality fiberscope observing the inside of an antique clock mechanism. Note how individual fibers are discernable, as each fiber only relays one part of the image. A fiberscope is a flexible optical fiber bundle with a lens on one end and an eyepiece or camera on the other. It is used to examine and inspect small, difficult-to ...
A principal -bundle, where denotes any topological group, is a fiber bundle: together with a continuous right action such that preserves the fibers of (i.e. if then for all ) and acts freely and transitively (meaning each fiber is a G-torsor) on them in such a way that for each and , the map sending to is a homeomorphism.
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