The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrödinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics. Titles in this series are co-published with International Press, Cambridge, MA.
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The Heisenberg group and its sub-Laplacian are at the cross-roads of many domains of analysis and geometry: nilpotent Lie groups theory, hypoelliptic second order partial differential equations, strongly pseudoconvex domains in complex analysis, probability theory of degenerate diffusion process, subRiemannian geometry, control theory and semiclassical analysis of quantum mechanics, see e.g., [13], [16], [30], [31], and [44]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geodesics that join the origin, modified complex action function, geodesics between the origin, one such geodesic, horizontality condition, smooth horizontal curve, geodesics increases, case sgn, real geodesics, complex geodesics, many geodesics, horizontal connectivity, geodesic completeness, areal velocity, connectivity theorem, geodesic corresponding, contact manifold, linear harmonic oscillator, geodesic connecting, classical action, horizontal curves, horizontal distribution Key Phrases - Capitalized Phrases (CAPs): (learn more)
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The Heisenberg group and its sub-Laplacian are at the cross-roads of many domains of analysis and geometry: nilpotent Lie groups theory, hypoelliptic second order partial differential equations, strongly pseudoconvex domains in complex analysis, probability theory of degenerate diffusion process, subRiemannian geometry, control theory and semiclassical analysis of quantum mechanics, see e.g., [13], [16], [30], [31], and [44]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geodesics that join the origin, modified complex action function, geodesics between the origin, one such geodesic, horizontality condition, smooth horizontal curve, geodesics increases, case sgn, real geodesics, complex geodesics, many geodesics, horizontal connectivity, geodesic completeness, areal velocity, connectivity theorem, geodesic corresponding, contact manifold, linear harmonic oscillator, geodesic connecting, classical action, horizontal curves, horizontal distribution Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Green New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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