By analogy with the octonionic electromagnetic and gravitational interactions, the octonionic strong and weak interactions and their quantum interplays are discussed. In weak interaction, the study deduces some conclusions of field sources and intermediate particles, which are consistent with the Dirac equation, Yang-Mills equation, some new intermediate particles and three kinds of colors etc....

We establish new existence and non-existence results for positive solutions of the Einstein–scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein–scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian con...

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

A new asymptotic expansion method is developed to separate the WheelerDeWitt equation into the time-dependent Schrödinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheele...

2 Derivation of the Hartree Equation in the Mean Field Limit 5 2.1 Mean Field Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Derivation of the Hartree Equation for Bounded Potentials . . . . . . . . . . . . . . . 7 2.3 Another Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Derivation of the Hartree Equation fo...

Green function and linear integrals of motion for a charged particle moving in electric field are discussed. Wigner function and tomogram of the ststionary states of the charge are obtained. Connection of quantum propagators for Schrödinger evolution equation, Moyal evolution equation and evolution equation in tomographic probability representation for charge moving in electric field is discussed.

4 Finite Difference Frequency Domain 7 4.1 Forcing Term Expressed as Deviation from a Background . . . . . . . . . . . . . . . 7 4.2 Setting up FDFD Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.3 Electric Field FDFD Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.4 Magnetic Field FDFD Equation . . . . . . . . . . . . . . . . . . . . . . ...

A new asymptotic expansion method is developed to separate the WheelerDeWitt equation into the time-dependent Schrödinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheele...

The wave type field equation θ = λθ, where θ is a coframe field on a space-time, was recently proposed to describe the gravity field. This equation has a unique static, spherical-symmetric, asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We show that the wave type field equation is satisfied by the pseudo-conformal frame if the conformal factor is determined by a sc...