The spacetime lattice model involves time lattice (static lattice) model and space lattice (dynamic lattice) model, both of which have the same lattices’ domains and the same fractal structures. The behaviors of the ...The spacetime lattice model involves time lattice (static lattice) model and space lattice (dynamic lattice) model, both of which have the same lattices’ domains and the same fractal structures. The behaviors of the space field obey the uncertainty relations, which gauge invariance shows the space field is a gauge field, making the electromagnetic field, gravitowagnetic field and the fermion field be gauged, and the Lorentz condition and Lorentz gauge are the intrinsic attributes of the spacetime. The quantization of the classical space field produces S bosons of spin-1, which stimulated states by charges and masses are respectively photons and gravitons. The S bosons in thermal excitation are immeasurable and their energies may be dark. The principle of partition of independent freedom degrees regularizes the degrees for all particles including neutrino, which must have mass. By the S bosons, we interpret newly the virtual photons. Using the spacetime lattice model, we investigate the breaking of the symmetry of the gradient fields and the symmetry of the curl fields for the potential functions of the space field, and the creations and the annihilations of the dark photons and the dark gravitons. The complexity requires us to rename the electroweak phase transition as electro-gravito-weak phase transition. Finally, antiparticles are discussed. Our approach for the lattice models is a kind of renormalization group theory, signifying the breaking of symmetries can be renormalized.展开更多
The present work is devoted to the study of bosons evolving in the frozen magnetar＇s crust endowed with an ultra-strong magnetic field orthogonal to an electric field, both described by periodic functions. We discuss...The present work is devoted to the study of bosons evolving in the frozen magnetar＇s crust endowed with an ultra-strong magnetic field orthogonal to an electric field, both described by periodic functions. We discuss the quantum tunneling process through the one-dimensional potential barrier along Oz. The solutions to the Klein- Gordon equation are expressed in terms of Mathieu＇s functions which, for computable particle＇s energy range, are turning from oscillatory to exponentially growing modes along Oz. Within the Jeffreys Wentzel Kramers- Brillouin framework, the transmission coefficient is computed for the particle momentum in the middle of the instability range.展开更多
文摘The spacetime lattice model involves time lattice (static lattice) model and space lattice (dynamic lattice) model, both of which have the same lattices’ domains and the same fractal structures. The behaviors of the space field obey the uncertainty relations, which gauge invariance shows the space field is a gauge field, making the electromagnetic field, gravitowagnetic field and the fermion field be gauged, and the Lorentz condition and Lorentz gauge are the intrinsic attributes of the spacetime. The quantization of the classical space field produces S bosons of spin-1, which stimulated states by charges and masses are respectively photons and gravitons. The S bosons in thermal excitation are immeasurable and their energies may be dark. The principle of partition of independent freedom degrees regularizes the degrees for all particles including neutrino, which must have mass. By the S bosons, we interpret newly the virtual photons. Using the spacetime lattice model, we investigate the breaking of the symmetry of the gradient fields and the symmetry of the curl fields for the potential functions of the space field, and the creations and the annihilations of the dark photons and the dark gravitons. The complexity requires us to rename the electroweak phase transition as electro-gravito-weak phase transition. Finally, antiparticles are discussed. Our approach for the lattice models is a kind of renormalization group theory, signifying the breaking of symmetries can be renormalized.
文摘The present work is devoted to the study of bosons evolving in the frozen magnetar＇s crust endowed with an ultra-strong magnetic field orthogonal to an electric field, both described by periodic functions. We discuss the quantum tunneling process through the one-dimensional potential barrier along Oz. The solutions to the Klein- Gordon equation are expressed in terms of Mathieu＇s functions which, for computable particle＇s energy range, are turning from oscillatory to exponentially growing modes along Oz. Within the Jeffreys Wentzel Kramers- Brillouin framework, the transmission coefficient is computed for the particle momentum in the middle of the instability range.
