摘要:

AbstractGeometric optics is analysed using the techniques of Presymplectic Geometry. We obtain the symplectic structure of the space of light rays in a medium of a non constant refractive index by reduction from a presymplectic structure, and using adapted coordinates, we find Darboux coordinates. The theory is illustrated with some examples and we point out some simple physical applications.

ISSN:0015-8208    

DOI:10.1002/prop.2190440302

出版商:WILEY‐VCH Verlag    

年代:1996

数据来源: WILEY

摘要:

AbstractEleven different types of “maximally superintegrable” Hamiltonian systems on the real hyperboloid (s0)2– (s1)2+ (s2)2– (s3)2= 1 are obtained. All of them correspond to a free Hamiltonian system on the homogeneous spaceSU(2, 2)/U(2, 1), but to reductions by different maximal abelian subgroups ofSU(2, 2). Each of the obtained systems allows 5 functionally independent integrals of motion, from which it is possible to form two or more triplets in involution (each of them includes the hamiltonian). The corresponding classical and quantum equations of motion can be solved by separation of variables on theO(2, 2

ISSN:0015-8208    

DOI:10.1002/prop.2190440303

出版商:WILEY‐VCH Verlag    

年代:1996

数据来源: WILEY

摘要:

AbstractWe construct a lagrangian geometric formulation for first‐order field theories using the canonical structures of first‐order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first‐order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining theEuler‐Lagrange equationsin two equivalent ways: as the result of a variational problem and developing thejet field formalism(which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter fo

ISSN:0015-8208    

DOI:10.1002/prop.2190440304

出版商:WILEY‐VCH Verlag    

年代:1996

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.2190440301

出版商:WILEY‐VCH Verlag    

年代:1996

数据来源: WILEY