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math-ph2013
Remark on the Serre-Swan theorem for graded manifolds
G. Sardanashvily
Combining the Batchelor theorem and the Serre-Swan theorem, we come to that, given a smooth manifold , a graded commutative -algebra $\cA$ is isomorphic to the stru…
math-ph2013
Deviation differential equations. Jacobi fields
G. Sardanashvily
Given a differential equation on a smooth fibre bundle Y, we consider its canonical vertical extension to that, called the deviation equation, on the vertical tangent bundle VY of…
math-ph2013
Fibre bundle formulation of time-dependent mechanics
G. Sardanashvily
We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations. Classical non-relativistic mechanics is formulated as a particular fiel…