Last edited by Mautilar
Saturday, August 8, 2020 | History

4 edition of Geometric formulation of classical and quantum mechanics found in the catalog.

Geometric formulation of classical and quantum mechanics

by G. Giachetta

  • 118 Want to read
  • 36 Currently reading

Published by World Scientific in Singapore, Hackensack, NJ, London .
Written in English

    Subjects:
  • Mechanics,
  • Mathematics,
  • Mathematical physics,
  • Differential Geometry,
  • Quantum theory

  • Edition Notes

    Includes bibliographical references (p. 369-376) and index.

    StatementGiovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily
    ContributionsMagiaradze, L. G., Sardanashvili, G. A. (Gennadiĭ Aleksandrovich)
    Classifications
    LC ClassificationsQC174.17.G46 G533 2011
    The Physical Object
    Paginationxi, 392 p. ;
    Number of Pages392
    ID Numbers
    Open LibraryOL25005955M
    ISBN 109814313726
    ISBN 109789814313728
    LC Control Number2011280752
    OCLC/WorldCa613430950

    geometric formulation of classical and quantum non-autonomous mechanics on fiber bundles over generalization of the Liouville–Arnold, Nekhoroshev and Mishchenko–Fomenko theorems on completely and partially integrable and superintegrable Hamiltonian systems to the case of non-compact invariant submanifolds [9]. (4) The GA formulation of spinors facilitates the treatment of rotations and rotational dynamics in both classical and quantum mechanics without coordinates or matrices. (5) GA provides fresh insights into the geometric structure of quantum mechanics with implications for .

    The standard books on classical mechanics are the books by Landau & Lifshitz [LL76] and the book by A. Arnold [AVW89]. The Lagrangian formulation In the Lagrangian formulation, a classical (at this point non-relativistic) system is described by its configuration space C (a Lagrangian manifold). A point q = {qi} i=1,N. classical, stochastic and quantum chaotic / turbulent systems on level of a 2nd year graduate statistical mechanics or quantum field theory course. Approach it the way that suits you best. All this book says is that time evolution adds up probability densities of initial states. Whenever a problem is linear, you solve it by finding its.

    Symplectic geometry is very useful for clearly and concisely formulating problems in classical physics and also for understanding the link between classical problems and their quantum counterparts. It is thus a subject of interest to both mathematicians and physicists, though they have approached the subject from different view points. Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.. If the present state of an object is known it is possible to predict by the laws of classical mechanics how it will move in the future (determinism) and how it has moved in the past (reversibility).


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Geometric formulation of classical and quantum mechanics by G. Giachetta Download PDF EPUB FB2

The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms Cited by: 9.

Plenty of books/papers have been written about differential geometry in relation with general relativity, string theory, classical/quantum/gauge field theory and classical mechanics (Mathematical Methods of Classical Mechanics by V.

Arnold comes to mind). The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. methods in classical and. The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mathematical formalism uses mainly a part of functional analysis, especially Hilbert space which is a kind of linear are distinguished from mathematical formalisms for physics theories developed prior to the early.

System Upgrade on Fri, Jun 26th, at 5pm (ET) During this period, our website will be offline for less than an hour but the E-commerce and registration of new users may not be available for up to 4 hours. Geometrical Formulation of Quantum Mechanics Abhay Ashtekar1,2 and Troy A.

Schilling1,3 1 Center for Gravitational Physics and Geometry Department of Physics, Penn State, University Park, PAUSA geometric, classical framework is to arise as a suitable limiting case.

However, deeper reflection shows that quantum mechanics is in. • Quantum mechanics is presented as classical Hamiltonian dynamics on a projective Hilbert space.

• Hannay’s classical adiabatic phase and angles are explained. • Review of Berry and Robbins' revolutionary approach to spin-statistics.

• A chapter on Examples and Applications paves the way for ongoing studies of geometric phases. Geometrical Formulation of Quantum Mechanics Abhay Ashtekar1;2 and Troy A.

Schilling1;3 1 Center for Gravitational Physics and Geometry Department of Physics, Penn State, University Park, PAUSA 2 Erwin Schr¨odinger International Institute for Mathematical Physics Boltzmanngasse 9, A Vienna, Austria.

Geometric formulation of quantum mechanics Hoshang Heydari Abstract Quantum mechanics is among the most important and successful mathemati-cal model for describing our physical reality. The traditional formulation of quan-tum mechanics is linear and algebraic.

In contrast classical mechanics is a geo. (ii) Geometric quantum mechanics s, G.W. Typical states and density matrices, Journal of Geometry and Physics, 8(), (). ar, A. and Schilling, T.A. Geometrical formulation of quantum mechanics.

In Alex Harvey, editor, On Einstein’s path: essays in honor of Engelbert Schucking, pages "The book under review provides a unified treatment of geometric phases in quantum and classical mechanics, which is mainly based on fiber bundle theory [T]his is a nice and well-written book about an interesting subject.

This book has a substantial, crystal clear introduction to quantum spin. This is followed by other kinds of quantum mechanics in the second half of the book. Tung, Group theory in physics (, ) Contains a lot of material on representations of groups, mostly applied to angular momentum and spin in quantum mechanics.

QM, non-relativistic. Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians.

This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's. The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted.

This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc. Search. Geometric Formulation of Classical and Quantum Mechanics, pp.

() No Access. Geometric Formulation of Classical and Quantum Mechanics. Metrics. Downloaded 27 times. States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a Uhler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics which, although equivalent to the standard algebraic formulation, has a very different appearance.

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states.

Geometric Formulation of Classical and Quantum Mechanics. Cached. {Giovanni Giachetta and Luigi Mangiarotti and Gennadi Sardanashvily}, title = {Geometric Formulation of Classical and Quantum Mechanics Abstract. A catalogue record for this book is available from the British Library.

For photocopying of material in this volume, please. Geometric formulation of non-autonomous mechanics. Article We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations.

Classical. devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation.

This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to advance the reader’s understanding.Introduction We have been experiencing since the s a process of “symplectization” of S- ence especially since it has been realized that symplectic geometry is the natural language of both classical mechanics in its Hamiltonian formulation, and of its re?nement,quantum mechanics.

The purposeof this bookis to providecorema- rial in the symplectic treatment of quantum mechanics. Hence one might hope to treat classical and quantum mechanics as contact topology problems. 2. Goal. We aim to develop a generally phase-spacetime covariant formulation of quantum mechanics.

We find a formulation of quantum mechanics in terms of intrinsic geometric structures on a contact manifold.