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

质点力学及协变汉密尔顿场论的拉格朗日形式与汉密尔顿形式扩展

理论物理学

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作      者
出  版 社
出版时间
2014年09月30日
装      帧
精装
ISBN
9789814578417
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页      码
300
语      种
英文
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图书简介
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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