عنوان

Applications of the theory of groups in mechanics and physics

شابک

9048165814

شابک

9789048165810

شماره

b540561

عنوان اصلي

Applications of the theory of groups in mechanics and physics

نام عام مواد

[Book]

نام نخستين پديدآور

by Petre P. Teodorescu and Nicolae A.P. Nicorovici.

محل نشرو پخش و غیره

Dordrecht ; London

نام ناشر، پخش کننده و غيره

Springer

تاریخ نشرو بخش و غیره

2011

نام خاص و کميت اثر

1 volume ; 24 cm.

عنوان فروست

Fundamental theories of physics, 140

متن يادداشت

Originally published: 2004.

متن يادداشت

1. Elements of General Theory of Groups.- 1 Basic notions.- 1.1 Introduction of the notion of group.- 1.2 Basic definitions and theorems.- 1.3 Representations of groups.- 1.4 The S3 group.- 2 Topological groups.- 2.1 Definitions. Generalities. Lie groups.- 2.2 Lie algebras. Unitary representations.- 3 Particular Abelian groups.- 3.1 The group of real numbers.- 3.2 The group of discrete translations.- 3.3 The SO(2) and Cn, groups.- 2. Lie Groups.- 1 The SO(3) group.- 1.1 Rotations.- 1.2 Parametrization of SO(3) and O(3).- 1.3 Functions defined on O(3). Infinitesimal generators.- 2 The SU(2) group.- 2.1 Parametrization of SU(2).- 2.2 Functions defined on SU(2). Infinitesimal generators.- 3 The SU(3) and GL(n, ?) groups.- 3.1 SU(3) Lie algebra.- 3.2 Infinitesimal generators. Parametrization of SU(3).- 3.3 The GL(n, ?) and SU(n) groups.- 4 The Lorentz group.- 4.1 Lorentz transformations.- 4.2 Parametrization and infinitesimal generators.- 3. Symmetry Groups of Differential Equations.- 1 Differential operators.- 1.1 The SO(3) and SO(n) groups.- 1.2 The SU(2) and SU(3) groups.- 2 Invariants and differential equations.- 2.1 Preliminary considerations.- 2.2 Invariant differential operators.- 3 Symmetry groups of certain differential equations.- 3.1 Central functions. Characters.- 3.2 The SO(3), SU(2), and SU(3) groups.- 3.3 Direct products of irreducible representations.- 4 Methods of study of certain differential equations.- 4.1 Ordinary differential equations.- 4.2 The linear equivalence method.- 4.3 Partial differential equations.- 4. Applications in Mechanics.- 1 Classical models of mechanics.- 1.1 Lagrangian formulation of classical mechanics.- 1.2 Hamiltonian formulation of classical mechanics.- 1.3 Invariance of the Lagrange and Hamilton equations.- 1.4 Noether's theorem and its reciprocal.- 2 Symmetry laws and applications.- 2.1 Lie groups with one parameter and with m parameters.- 2.2 The Symplectic and Euclidean groups.- 3 Space-time symmetries. Conservation laws.- 3.1 Particular groups. Noether's theorem.- 3.2 The reciprocal of Noether's theorem.- 3.3 The Hamilton-Jacobi equation for a free particle.- 4 Applications in the theory of vibrations.- 4.1 General considerations.- 4.2 Transformations of normal coordinates.- 5. Applications in the Theory of Relativity and Theory of Classical Fields.- 1 Theory of Special Relativity.- 1.1 Preliminary considerations.- 1.2 Applications in the theory of Special Relativity.- 2 Theory of electromagnetic field.- 2.1 Noether's theorem for the electromagnetic field.- 2.2 Conformal transformations in four dimensions.- 3 Theory of gravitational field.- 3.1 General equations.- 3.2 Conservation laws in the Riemann space.- 6. Applications in Quantum Mechanics and Physics of Elementary Particles.- 1 Non-relativistic quantum mechanics.- 1.1 Invariance properties of quantum systems.- 1.2 The angular momentum. The spin.- 2 Internal symmetries of elementary particles.- 2.1 The isospin and the SU(2) group.- 2.2 The unitary spin and the SU(3) group.- 3 Relativistic quantum mechanics.- 3.1 Basic equations. Symmetry groups.- 3.2 Elementary particle interactions.- References.

موضوع مستند نشده

Group theory.

موضوع مستند نشده

Mathematical physics.

موضوع مستند نشده

Quantum theory.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Petre P. Teodorescu and Nicolae A.P. Nicorovici.

مستند نام اشخاص تاييد نشده

Nicolae A Nicorovici

مستند نام اشخاص تاييد نشده

P P Teodorescu

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y