arXiv subjects

M. Katanaev

Publications and source records attributed to M. Katanaev.

3 recordsLinked to original sources

arXiv2021

Global conformal gauge in string theory

It was supposed for fifty years that the conformal gauge in string theory exists globally on the whole string world sheet. In fact, almost all results were obtained under this assumption. However, this statement was proved only locally in some neighbourhood of an arbitrary point on the worldsheet, and its extension is far from being obvious. In the present paper we prove that the conformal gauge does exists globally on the string worldsheet represented by an infinite strip with straight parallel boundaries.

physics.gen-ph↗

arXiv2019

Point disclinations in the Chern-Simons geometric theory of defects

We use the Chern-Simons action for a SO(3)-connection for the description of point disclinations in the geometric theory of defects. The most general spherically symmetric SO(3)-connection with zero curvature is found. The corresponding orthogonal spherically symmetric SO(3) matrix and n-field are computed. Two examples of point disclinations are described.

math-ph↗

arXiv2015

On homogeneous and isotropic universe

We give a simple example of spacetime metric, illustrating that homogeneity and isotropy of space slices at all moments of time is not obligatory lifted to a full system of six Killing vector fields in spacetime, thus it cannot be interpreted as a symmetry of a four dimensional metric. The metric depends on two arbitrary and independent functions of time. One of these functions is the usual scale factor. The second function cannot be removed by coordinate transformations. We prove that it must be equal to zero, if the metric satisfies Einstein's equations and the matter energy momentum tensor is homogeneous and isotropic. A new, equivalent, definition of homogeneous and isotropic spacetime is given.

gr-qc↗