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Generalized Hamiltonian Formalism for Field Theory

1995 Science
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Release : 1995
Genre : Science
Kind : eBook
Book Rating : 457/5 ( reviews)

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Book Synopsis Generalized Hamiltonian Formalism for Field Theory by : G. Sardanashvily

Download or read book Generalized Hamiltonian Formalism for Field Theory written by G. Sardanashvily. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.

Generalized Classical Mechanics and Field Theory

2011-08-30 Science
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Release : 2011-08-30
Genre : Science
Kind : eBook
Book Rating : 239/5 ( reviews)

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Book Synopsis Generalized Classical Mechanics and Field Theory by : M. de León

Download or read book Generalized Classical Mechanics and Field Theory written by M. de León. This book was released on 2011-08-30. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to discuss the present situation of Lagrangian and Hamiltonian formalisms involving higher order derivatives. The achievements of differential geometry in formulating a more modern and powerful treatment of these theories is described and an extensive review of the development of these theories in classical language is also given.

Studies in Generalized Hamiltonian Formalism

2012-04
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Release : 2012-04
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Kind : eBook
Book Rating : 305/5 ( reviews)

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Book Synopsis Studies in Generalized Hamiltonian Formalism by : Mohammed Ashraful Islam

Download or read book Studies in Generalized Hamiltonian Formalism written by Mohammed Ashraful Islam. This book was released on 2012-04. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theories are quite difficult. The successes achieved by using quantum field theories are rather limited because in these theories one faces various difficulties. Later Dirac introduced an alternative process to quantize the fields. He introduced Hamiltonian equations of motion from Lagrangian to describe the laws of mechanics and gravitation. It has wide application in classical mechanics, quantum mechanics and quantum field theory, as well as in general relativity etc. One may deal with Hamiltonian in general frameworks as well as oscillatory systems.

New Lagrangian And Hamiltonian Methods In Field Theory

1997-12-18 Science
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Release : 1997-12-18
Genre : Science
Kind : eBook
Book Rating : 085/5 ( reviews)

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Book Synopsis New Lagrangian And Hamiltonian Methods In Field Theory by : Giovanni Giachetta

Download or read book New Lagrangian And Hamiltonian Methods In Field Theory written by Giovanni Giachetta. This book was released on 1997-12-18. Available in PDF, EPUB and Kindle. Book excerpt: This book incorporates 3 modern aspects of mathematical physics: the jet methods in differential geometry, Lagrangian formalism on jet manifolds and the multimomentum approach to Hamiltonian formalism. Several contemporary field models are investigated in detail.This is not a book on differential geometry. However, modern concepts of differential geometry such as jet manifolds and connections are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied at the general level including a treatment of Hamiltonian formalism on composite fiber manifolds. The book presents new geometric methods and results in field theory.

Extended Lagrange and Hamilton Formalism for Point Mechanics and Covariant Hamilton Field Theory

2017-05-31 Science
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Release : 2017-05-31
Genre : Science
Kind : eBook
Book Rating : 417/5 ( reviews)

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Book Synopsis Extended Lagrange and Hamilton Formalism for Point Mechanics and Covariant Hamilton Field Theory by : Jurgen Struckmeier

Download or read book Extended Lagrange and Hamilton Formalism for Point Mechanics and Covariant Hamilton Field Theory written by Jurgen Struckmeier. This book was released on 2017-05-31. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an explicitly covariant canonical formalism that is devised in the usual mathematical language of standard textbooks on classical dynamics. It elaborates on important questions: How do we convert the entire canonical formalism of Lagrange and Hamilton that are built upon Newton's concept of an absolute time into a relativistically correct form that is appropriate to our present knowledge? How do we treat the space-time variables in a Hamiltonian Field Theory on equal footing as in the Lagrangian description of field theory without introducing a new mathematical language? How can a closed covariant canonical gauge theory be obtained from it? To answer the last question, the theory of homogenous and inhomogeneous gauge transformations is worked out in this book on the basis of the canonical transformation theory for fields elaborated before. In analogy to the treatment of time in relativistic point mechanics, the canonical formalism in field theory is further extended to a space-time that is no longer fixed but is also treated as a canonical variable. Applied to a generalized theory of gauge transformations, this opens the door to a new approach to general relativity.

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