Methods of Differential Geometry in Classical Field Theories: k-Symplectic and k-Cosymplectic Approaches by Manuel de León

Methods of Differential Geometry in Classical Field Theories: k-Symplectic and k-Cosymplectic…

byManuel de León, Modesto Salgado, Silvia Vilariño

Kobo ebook | August 28, 2015

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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
Title:Methods of Differential Geometry in Classical Field Theories: k-Symplectic and k-Cosymplectic…Format:Kobo ebookPublished:August 28, 2015Publisher:World Scientific Publishing CompanyLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9814699772

ISBN - 13:9789814699778

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