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Lectures on selected topics in mathematical physics : introduction to lie theory with applications /
This book provides an introduction to Lie theory for first-year graduate students and professional physicists who may not have come across the theory in their studies. It is an overview of the theory of finite groups, a brief description of a manifold, and an informal development of the theory of on...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) :
Morgan & Claypool Publishers,
[2017]
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| Colección: | IOP (Series). Release 3.
IOP concise physics. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface
- Introduction
- 1. Groups
- 1.1. Permutations and symmetries
- 1.2. Subgroups and classes
- 1.3. Representations
- 1.4. Orthogonality
- 2. Lie groups
- 2.1. Lie groups as manifolds
- 2.2. Lie groups as groups of transformations or substitutions
- 2.3. Infinitesimal generators
- 2.4. Generator example: Lorentz boost
- 2.5. Transformations acting in three or more dimensions
- 2.6. Changing coordinates
- 2.7. Changing variables in the generator
- 2.8. Invariant functions, invariant curves, and groups that permute curves in a family
- 2.9. Canonical coordinates for a one-parameter group
- 3. Ordinary differential equations
- 3.1. Prolongation of the group generator and a symmetry criterion
- 3.2. Reformulation of symmetry in terms of partial differential operators
- 3.3. Symmetries in terms of A
- 3.4. Note on evaluating commutators
- 3.5. Symmetries of first-order DEs
- 3.6. Tabulating DEs according to groups they admit
- 3.7. Lie's integrating factor
- 3.8. Finding symmetries of a second order
- 3.9. Using a symmetry to reduce the order
- 3.10. Classical mechanics: N<U+008A>other's theorem.