Download e-book for kindle: Mathematical Topics Between Classical and Quantum Mechanics by Nicholas P. Landsman

By Nicholas P. Landsman

ISBN-10: 038798318X

ISBN-13: 9780387983189

This monograph attracts on traditions: the algebraic formula of quantum mechanics and quantum box idea, and the geometric thought of classical mechanics. those are mixed in a unified remedy of the speculation of Poisson algebras of observables and natural nation areas with a transition likelihood. the idea of quantization and the classical restrict is mentioned from this angle. A prototype of quantization comes from the analogy among the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel among aid of symplectic manifolds in classical mechanics and brought about representations of teams and C*- algebras in quantum mechanics performs an both very important function. Examples from physics contain limited quantization, curved areas, magnetic monopoles, gauge theories, massless debris, and $theta$- vacua. The ebook could be obtainable to mathematicians with a few previous wisdom of classical and quantum! mechanics, to mathematical physicists and to theoretical physicists who've a few historical past in useful research.

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392–4). 1 On the relativistic constraints According to the standard understanding of special relativity, there is no foliation of spacetime into parallel spacelike hyperplanes that is preferred by the laws of physics: All foliations of spacetime are on equal footing. Moreover, special relativity also 22 JOSEPH BERKOVITZ AND MEIR HEMMO requires that the descriptions of physical reality in different coordinate systems will be consistent with each other. In the special relativistic spacetime – the Minkowski spacetime – this requirement is satisfied when the descriptions of physical reality in different foliations of spacetime into parallel spacelike hyperplanes (and accordingly in different inertial frames of reference) are related to each other by the Lorentz transformations.

1 On the relativistic constraints According to the standard understanding of special relativity, there is no foliation of spacetime into parallel spacelike hyperplanes that is preferred by the laws of physics: All foliations of spacetime are on equal footing. Moreover, special relativity also 22 JOSEPH BERKOVITZ AND MEIR HEMMO requires that the descriptions of physical reality in different coordinate systems will be consistent with each other. In the special relativistic spacetime – the Minkowski spacetime – this requirement is satisfied when the descriptions of physical reality in different foliations of spacetime into parallel spacelike hyperplanes (and accordingly in different inertial frames of reference) are related to each other by the Lorentz transformations.

Brown. The origins of length contraction: I the FitzGerald-Lorentz deformation hypothesis. American Journal of Physics, 69:1044–1054, 2001. E-prints: arXive:gr-qc/0104032; PITT-PHILSCI 218. Harvey R. Brown. Einstein’s misgivings about his 1905 formulation of special relativity. European Journal of Physics, 26:S85S90, special Einstein issue, 2005a. Harvey R. Brown. Physical relativity: space-time structure from a dynamical perspective. Oxford University Press, Oxford, 2005b. Harvey R. Brown and Oliver Pooley.

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Mathematical Topics Between Classical and Quantum Mechanics by Nicholas P. Landsman


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