Weyl geometry

Einstein { Weyl Geometry , the dKP

Isotropic cosmologies in Weyl geometry

We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a twofluid source. We write the equations as a two-dimensional dynamical system and analyze the qualitative, asymptotic behavior of the models. We examine the possibility that in certain theories the Weyl 1-f...

De Donder-weyl Equations and Multisymplectic Geometry

Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral mani-folds of Hamiltonean multivectorfields. In contrast to mechanics, solutions cannot be described by points in the multi-symplectic phase space. Foliations ...

Noncommutative Differential Geometry of Generalized Weyl Algebras

Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p; q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p; q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p; q) are constructed, and three-dimensional first-...

Weyl geometry approach to describe planetary systems

In the present work we show that planetary mean distances can be calculated through considering the Weyl geometry. We interpret the Weyl gauge field as a vector field associated with the hypercharge of the particles and apply the gauge concept of the Weyl geometry. The results obtained are shown to agree with the observed orbits of all the planets and of the asteroid belt in the solar system, w...