Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T13:25:21Z No. of bitstreams: 1 arquivototal.pdf: 1212419 bytes, checksum: 6d3ca7625ab07b583f3f68045187a552 (MD5) / Made available in DSpace on 2017-09-12T13:25:21Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1212419 bytes, checksum: 6d3ca7625ab07b583f3f68045187a552 (MD5) Previous issue date: 2016-02-25 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In 1918 the German Hermann Weyl developed a unified theory of gravitation and electro­magnetism becoming geometrical both interactions, that is, he associated the potential elec­tromagnetic a 1-form a, after considering that the length of a vector is not preserved under parallel transport as well as with the direction, this also meant that the covariant derivatives of the metric tensor ceased to be null becoming Vag" = a, The gravitational and electromagnetic field equations are obtained from the action I = f (R2 ± v Ft" ) —gd4x in a gauge any and "natural gauge"R = A = constant taking into account that they, as well as the action, should be both invariant under coordinate transformations as invariant under the gauge transformations introduced, namely, gliv = of gin, and di, = cp.+ hi, actually, the first person to speak in scale invariance in physics was the Weyl himself in his article. It is also found that the solutions to the emptiness of Einstein's field equations are also solutions of the corresponding Weyl's field equations. Finally it is shown that the Weyl affine geo­desic may not come from a variational principle by analysing the Helmholtz conditions for the inverse problem of the calculus of variations and discusses about Einstein's criticism of the theory, on which it is concluded that the even seized an inadequate definition of proper time to give his opinion on the work of Weyl, thus, a problem to be solved was to find a good definition of proper time, which leaves open a final version of the Weyl theory. / Em 1918 o alem-do Hermann Weyl desenvolveu sua teoria de unificndo entre gravitacao e eletromagnetismo geometrizando ambas as internOes, isto é, ele associou o potencial eletromagnetico a uma 1-forma a, depois de ter considerado que o comprimento de um vetor nao preserva-se sob transporte paralelo assim como acontece com a direcao, isso tambem fez com que a derivada covariante do tensor metrico deixasse de ser nula tornando­se V agii, = glivaa. As equagOes de campo gravitacionais e eletromagneticas sdo obti­das da nao I = f (R2 ±AF,,,,Filv)\/—gd4x em um calibre qualquer e no "calibre natural" R = A = const ante levando em conta que elas, assim como a nao, devem ser tanto invari­antes por transformnOes de coordenadas como invariantes sob as transformnOes de calibre introduzidas, a saber, gliv = of gin, e di, = al, + hi, na verdade, a primeira pessoa a falar em invarifincia de escala na fisica foi o prOprio Weyl em seu artigo. Tambem é verificado que as solucOes para o vazio das equagOes de campo de Einstein tambem sac) solucOes das equnOes de campo de Weyl correspondentes. Por fim mostra-se que as geodesicas afins de Weyl nao podem advir de um princfpio variacional atraves da analise das condicOes de Helmholtz para o problema inverso do calculo de varinOes e discute-se sobre a critica de Einstein a teoria, onde conclui-se que o mesmo se apoderou de uma definicao inadequada de tempo proprio para dar seu parecer sobre o trabalho de Weyl, assim, um problema a ser resolvido seria encontrar uma boa definicao de tempo pr6prio, o que deixa em aberto uma versdo final da teoria de Weyl.