ON THE LEGENDRE TRANSFORMATION FOR A CLASS OF NONREGULAR HIGHER-ORDER LAGRANGIAN FIELD-THEORIES

被引:19
作者
MAGNANO, G
FERRARIS, M
FRANCAVIGLIA, M
机构
[1] UNIV CAGLIARI,DIPARTIMENTO MATEMAT,I-09124 CAGLIARI,ITALY
[2] UNIV TURIN,IST FIS MATEMAT LL LAGRANGE,I-10123 TURIN,ITALY
关键词
D O I
10.1063/1.528925
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In the framework of higher-order calculus of variations, the generalized Legendre transformation for a wide class of Lagrangians is considered, which depend in a nonregular way on the derivatives of maximal order. A rigorous theory is discussed for Lagrangians depending on a constant rank set of affine combinations of these derivatives. This allows the reduction of the Poincaré-Cartan formalism and the Hamiltonian formalism to the appropriate constraint in the appropriate phase space of the problem. The case considered here covers many important physical examples, such as the Yang-Mills theories (at order one) and relativistic metric theories of gravitation (at order two). © 1990 American Institute of Physics.
引用
收藏
页码:378 / 387
页数:10
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