Methods of Differential Geometry in Classical Field Theories

k-Symplectic and k-Cosymplectic Approaches

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