Quantum Physics, Relativity, and Complex Spacetime
by Gerald Kaiser
Publisher: University of Massachusetts at Lowell 2003
Number of pages: 252
A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.
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by L. Schwartz - Tata Institute of Fundamental Research
Topics covered: Differentiable Manifolds; C maps, diffeomorphisms. Effect of a map; The Tensor Bundles; Existence and uniqueness of the exterior differentiation; Manifolds with boundary; Integration on chains; Some examples of currents; etc.
by Daniele Angella, Cristiano Spotti - arXiv.org
We present classical and recent results on Kaehler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for author's course.
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The intent is not to give a thorough treatment of the algebraic and differential geometry of complex manifolds, but to introduce the reader to material of current interest as quickly as possible. A number of interesting examples is provided.
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Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.