advanced_tools:jet_bundles
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
|
advanced_tools:jet_bundles [2017/11/08 16:59] jakobadmin [Student] |
advanced_tools:jet_bundles [2017/12/04 08:01] 127.0.0.1 external edit |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| + | <blockquote> | ||
| + | |||
| + | |||
| + | Given a [[advanced_tools:fiber_bundles|field bundle]] [...], we know what type of quantities the corresponding fields assign to a given spacetime point. Among all consistent such field configurations, some are to qualify as those that “may occur in reality” if we think of the field theory as a means to describe parts of the observable universe. Moreover, if the reality to be described does not exhibit “action at a distance” then admissibility of its field configurations should be determined over arbitrary small spacetime regions, in fact over the infinitesimal neighbourhood of any point. This means equivalently that the realized field configurations should be those that satisfy a [[:equations|specific differential equation]], hence an equation between the value of its derivatives at any spacetime point. | ||
| + | |||
| + | In order to formalize this, it is useful to first collect all the possible derivatives that a field may have at any given point into one big space of “field derivatives at spacetime points”. This collection is called the jet bundle of the field bundle.<cite>https://ncatlab.org/nlab/show/field+%28physics%29#AFirstIdeaOfQuantumFields</cite></blockquote> | ||
| <tabbox Layman> | <tabbox Layman> | ||
| Line 19: | Line 25: | ||
| {{ :advanced_tools:schreiber1.png?nolink |}} | {{ :advanced_tools:schreiber1.png?nolink |}} | ||
| | | ||
| - | Therefore every section $\phi$ of $E$ | + | **Therefore every section $\phi$ of $E$ |
| yields a section $j^\infty(\phi)$ of the jet bundle, given by $\phi$ | yields a section $j^\infty(\phi)$ of the jet bundle, given by $\phi$ | ||
| - | and all its higher order derivatives. | + | and all its higher order derivatives.** |
| {{ :advanced_tools:schreiber2.png?nolink |}} | {{ :advanced_tools:schreiber2.png?nolink |}} | ||
advanced_tools/jet_bundles.txt · Last modified: 2018/05/03 11:45 by paul
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
