By Vladimir G Ivancevic

ISBN-10: 1429496525

ISBN-13: 9781429496520

ISBN-10: 9812706143

ISBN-13: 9789812706140

This graduate-level monographic textbook treats utilized differential geometry from a contemporary medical viewpoint. Co-authored by way of the originator of the realm s major human movement simulator Human Biodynamics Engine , a posh, 264-DOF bio-mechanical method, modeled by means of differential-geometric instruments this can be the 1st booklet that mixes sleek differential geometry with a large spectrum of purposes, from smooth mechanics and physics, through nonlinear regulate, to biology and human sciences. The booklet is designed for a two-semester path, which supplies mathematicians various functions for his or her idea and physicists, in addition to different scientists and engineers, a powerful conception underlying their types.

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**Example text**

9 Application: Cerebellum as a Neural Path–Integral . . . . . . . . . . 1 Spinal Autogenetic Reflex Control . . 2 Cerebellum – the Comparator . . . 3 Hamiltonian Action and Neural Path Integral . . . . . . . . . 10 Path Integrals via Jets: Perturbative Quantum Fields . . . . . . . . . . . . . 4 Sum over Geometries and Topologies . . . . . . 1 Simplicial Quantum Geometry . . . . . . 2 Discrete Gravitational Path Integrals . . . . 3 Regge Calculus .

2 Interactions . . . . . . . . 3 Loop Expansion – Topology of Closed Surfaces . . . . . . . . . 5 Transition Amplitudes for Strings . . . . . 7 More General Actions . . . . . . . . 8 Transition Amplitude for a Single Point Particle . 9 Witten’s Open String Field Theory . . . . 1 Operator Formulation of String Field Theory . . . . . . . . . 2 Open Strings in Constant B−Field Background . . . . . . . . 3 Construction of Overlap Vertices .

10 Application: Adaptive Path Integral . . 2 Path Integral History . . . . . . . . . 1 Extract from Feynman’s Nobel Lecture . . 2 Lagrangian Path Integral . . . . . . 3 Hamiltonian Path Integral . . . . . . 4 Feynman–Kac Formula . . . . . . . 5 Itˆ o Formula . . . . . . . . . . 3 Standard Path–Integral Quantization . . . . . 1 Canonical versus Path–Integral Quantization . 2 Application: Particles, Sources, Fields and Gauges . . . . . . . . .

### Applied differential geometry. A modern introduction by Vladimir G Ivancevic

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