Methods of Differential Geometry in Classical Field Theories
k-Symplectic and k-Cosymplectic Approaches
Nonfiction, Science & Nature, Mathematics, Geometry, Applied
| Author: | Manuel de León, Modesto Salgado, Silvia Vilariño | ISBN: | 9789814699778 |
| Publisher: | World Scientific Publishing Company | Publication: | August 28, 2015 |
| Imprint: | WSPC | Language: | English |
| Author: | Manuel de León, Modesto Salgado, Silvia Vilariño |
| ISBN: | 9789814699778 |
| Publisher: | World Scientific Publishing Company |
| Publication: | August 28, 2015 |
| Imprint: | WSPC |
| Language: | English |
This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism.
It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject.
Contents:
-
A Review of Hamiltonian and Lagrangian Mechanics:
- Hamiltonian and Lagrangian Mechanics
-
k-Symplectic Formulation of Classical Field Theories:
- k-Symplectic Geometry
- k-Symplectic Formalism
- Hamiltonian Classical Field Theory
- Hamilton–Jacobi Theory in k-Symplectic Field Theories
- Lagrangian Classical Field Theories
- Examples
-
k-Cosymplectic Formulation of Classical Field Theories:
- k-Cosymplectic Geometry
- k-Cosymplectic Formalism
- Hamiltonian Classical Field Theories
- Hamilton–Jacobi Equation
- Lagrangian Classical Field Theories
- Examples
- k-Symplectic Systems versus Autonomous k-Cosymplectic Systems
-
Relationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism:
- Multisymplectic Formalism
-
Appendices:
- Symplectic Manifolds
- Cosymplectic Manifolds
- Glossary of Symbols
Readership: Graduate students and researchers in classical field theories.
Key Features:
- This book contains for the first time this new geometric approach to Classical Field Theory. Up to now the theory is disseminated in several journal papers
- The subject is very active in the last years
- There are many open problems in Classical Field Theories to be attacked using this new formalism
This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism.
It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject.
Contents:
-
A Review of Hamiltonian and Lagrangian Mechanics:
- Hamiltonian and Lagrangian Mechanics
-
k-Symplectic Formulation of Classical Field Theories:
- k-Symplectic Geometry
- k-Symplectic Formalism
- Hamiltonian Classical Field Theory
- Hamilton–Jacobi Theory in k-Symplectic Field Theories
- Lagrangian Classical Field Theories
- Examples
-
k-Cosymplectic Formulation of Classical Field Theories:
- k-Cosymplectic Geometry
- k-Cosymplectic Formalism
- Hamiltonian Classical Field Theories
- Hamilton–Jacobi Equation
- Lagrangian Classical Field Theories
- Examples
- k-Symplectic Systems versus Autonomous k-Cosymplectic Systems
-
Relationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism:
- Multisymplectic Formalism
-
Appendices:
- Symplectic Manifolds
- Cosymplectic Manifolds
- Glossary of Symbols
Readership: Graduate students and researchers in classical field theories.
Key Features:
- This book contains for the first time this new geometric approach to Classical Field Theory. Up to now the theory is disseminated in several journal papers
- The subject is very active in the last years
- There are many open problems in Classical Field Theories to be attacked using this new formalism
