|
" Applications of the theory of groups in mechanics and physics "
by Petre P. Teodorescu and Nicolae A.P. Nicorovici.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
720861
|
| Doc. No
|
:
|
b540561
|
| Main Entry
|
:
|
by Petre P. Teodorescu and Nicolae A.P. Nicorovici.
|
| Title & Author
|
:
|
Applications of the theory of groups in mechanics and physics\ by Petre P. Teodorescu and Nicolae A.P. Nicorovici.
|
| Publication Statement
|
:
|
Dordrecht ; London: Springer, 2011
|
| Series Statement
|
:
|
Fundamental theories of physics, 140
|
| Page. NO
|
:
|
1 volume ; 24 cm.
|
| ISBN
|
:
|
9048165814
|
|
|
:
|
: 9789048165810
|
| Notes
|
:
|
Originally published: 2004.
|
| Contents
|
:
|
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.
|
| Subject
|
:
|
Group theory.
|
| Subject
|
:
|
Mathematical physics.
|
| Subject
|
:
|
Quantum theory.
|
| LC Classification
|
:
|
QC20.7.G76B974 2011
|
| Added Entry
|
:
|
Nicolae A Nicorovici
|
|
|
:
|
P P Teodorescu
|
| |