Belal E. BaaquieCambridge University Press, 3/27/2014EAN 9781107009790, ISBN10: 1107009790Hardcover, 436 pages, 24.4 x 17 x 2.4 cmLanguage: EnglishProviding a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.1. SynopsisPart I. Fundamental Principles2. The mathematical structure of quantum mechanics3. Operators4. The Feynman path integral5. Hamiltonian mechanics6. Path integral quantizationPart II. Stochastic Processes7. Stochastic systemsPart III. Discrete Degrees of Freedom8. Ising model9. Ising modelmagnetic field10. FermionsPart IV. Quadratic Path Integrals11. Simple harmonic oscillators12. Gaussian path integralsPart V. Action with Acceleration13. Acceleration Lagrangian14. Pseudo-Hermitian Euclidean Hamiltonian15. Non-Hermitian HamiltonianJordan blocks16. The quartic potentialinstantons17. Compact degrees of freedomIndex.
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