TY - JOUR

T1 - Comparison of basic equations of the Kaluza–Klein theory with the nonholonomic model of space–time of the sub-Lorentzian geometry

AU - Krym, V.R.

PY - 2023

Y1 - 2023

N2 - The field equations of gravity coupled to electromagnetism and equations of motion of a charged particle are part of the Kaluza–Klein theory where general relativity is extended to five dimensions. These equations can also be obtained if nonholonomic constrains are imposed on the 5-vector of particle’s velocity. Hence, further development of the general relativity theory can be sub-Riemannian (or sub-Lorentzian) geometry. Gauge transformations become a special case of coordinate transformations in both the Kaluza–Klein theory and the nonholonomic model. Sub-Riemannian geodesics are proved to be equations of motion of a charged particle. The Dirac operator can be extended for a 5-dimensional manifold as a first-order differential operator. Since the base manifold in physics contains the electromagnetic gauge group U(1), the eigenvalues of the charge operator are always an integer multiplied by the fundamental electric charge.

AB - The field equations of gravity coupled to electromagnetism and equations of motion of a charged particle are part of the Kaluza–Klein theory where general relativity is extended to five dimensions. These equations can also be obtained if nonholonomic constrains are imposed on the 5-vector of particle’s velocity. Hence, further development of the general relativity theory can be sub-Riemannian (or sub-Lorentzian) geometry. Gauge transformations become a special case of coordinate transformations in both the Kaluza–Klein theory and the nonholonomic model. Sub-Riemannian geodesics are proved to be equations of motion of a charged particle. The Dirac operator can be extended for a 5-dimensional manifold as a first-order differential operator. Since the base manifold in physics contains the electromagnetic gauge group U(1), the eigenvalues of the charge operator are always an integer multiplied by the fundamental electric charge.

KW - Kaluza–Klein theory

KW - nonholonomic distributions

KW - sub-Riemannian geometry

KW - Schouten curvature

KW - Dirac operator

KW - quantization of the electric charge

M3 - Article

VL - 38

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 9-10

M1 - 2350049

ER -