Differential Forms and Integration
Physics is expressed in the language of differential equations (e.g., Maxwell, Dirac, Yang-Mills, Einstein, etc.). Differential equations live on differentiable manifolds and differentiable manifolds have topologies that influence not only the solutions to differential equations defined on them, but even the type of equation that one can define on them. At some naive level then it is perhaps not surprising that topology and physics interact. The profound depth of this interaction in recent years, however, has made it abundantly clear that the naive level is not the appropriate one from which to view this.
KeywordsDifferential Form Measure Zero Coordinate Function Dual Basis Real Vector Space
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