This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klei...This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.展开更多
In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws fo...In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws for such system was deduced. The preliminary applications of the GBIVCS to the case for some models of field theories was given. The Dirac constraint of such system was discussed.展开更多
In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that t...In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that the field equations of the gravitational field, the Newton’s second law of classical dynamics, and the Maxwell field equations of the electromagnetic field all share the same mathematical structure. Consequently, the Ricci flow itself may be regarded as dynamical equations used to describe physical processes associated with the gravitational field, such as the process of smoothing out irregularities of distribution of matter in space.展开更多
文摘This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.
基金This work was supported by Beijing Science Foundation of the People's Republie of China.
文摘In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws for such system was deduced. The preliminary applications of the GBIVCS to the case for some models of field theories was given. The Dirac constraint of such system was discussed.
文摘In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that the field equations of the gravitational field, the Newton’s second law of classical dynamics, and the Maxwell field equations of the electromagnetic field all share the same mathematical structure. Consequently, the Ricci flow itself may be regarded as dynamical equations used to describe physical processes associated with the gravitational field, such as the process of smoothing out irregularities of distribution of matter in space.
