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Chern–Simons Form
In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose. Definition Given a manifold and a Lie algebra valued Multilinear form, 1-form \mathbf over it, we can define a family of Multilinear form, ''p''-forms: In one dimension, the Chern–Simons Multilinear form, 1-form is given by :\operatorname [ \mathbf ]. In three dimensions, the Chern–Simons 3-form is given by :\operatorname \left[ \mathbf \wedge \mathbf-\frac \mathbf \wedge \mathbf \wedge \mathbf \right] = \operatorname \left[ d\mathbf \wedge \mathbf + \frac \mathbf \wedge \mathbf \wedge \mathbf\right]. In five dimensions, the Chern–Simons 5-form is given by : \begin & \operatorname \left[ \mathbf\wedge\mathbf \wedge \mathbf-\frac \mathbf \wedge\mathbf\wedge\mathbf\wedge\mathbf +\frac \mathbf \wedge \mathbf \w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
