Considering a n-dimensional general spacetime, we deduce its 4-dimensional Einstein equation and Friedman equations, and discover a general dual relation between the scale factor $a(t)$ of our universe and the scale factor $B(t)$ of extra dimensions.
Based on the dual relation equation, predictions of shrinking of extra dimensions and free of singularity problem of our universe are given. Therefore, solution to initial singularity paradox of our universe is achieved. Because the dual relation is general, this Letter discovers that it is just the extra dimensional shrinking contribution that results in our universes expanding in terms of the dual relation in the bulk space, and actually the dual relation is deduced doesnt depend on the 4-dimensional matter concrete Lagrangian, these are key important for a lot of future relative investigations.
We first review some aspects of gravitational wave and the thermodynamic expression of Einstein field equations, these achieved conclusions allow people to think of Einsteins gravitational wave as a kind of sound wave in ordinary gas which propagates
as an adiabatic compression wave. In the following, using the properties of photon gas in white wall box, we find an analogous relationship between ordinary gas and photon gas through sound velocity formula. At last, by taking the ordinary gas as an intermediary, we find that gravitational wave is analogous to photon gas, or equally, gravitons are analogous to photons although they are different in some ways such as spins and coupling strengths, and these different properties dont affect their propagation speeds. Utilizing this analogous relationship, we achieve the gas model of gravitons and this model naturally gives out the light speed of gravitons
This Letter, i.e. for the first time, proves that a general invariant velocity is originated from the principle of special relativity, namely, discovers the origin of the general invariant velocity, and when the general invariant velocity is taken as
the invariant light velocity in current theories, we get the corresponding special theory of relativity. Further, this Letter deduces triple special theories of relativity in cosmology, and cancels the invariant presumption of light velocity, it is proved that there exists a general constant velocity K determined by the experiments in cosmology, for K > 0, = 0 and < 0, they correspond to three kinds of possible relativistic theories in which the special theory of relativity is naturally contained for the special case of K > 0, and this Letter gives a prediction that, for K < 0, there is another likely case satisfying the principle of special relativity for some special physical systems in cosmology, in which the relativistic effects observed would be that the moving body would be lengthened, moving clock would be quickened. And the point of K = 0 is a bifurcation point, through which it gives out three types of possible universes in the cosmology (or multiverse). When a kind of matter with the maximally invariant velocity that may be superluminal or equal to light velocity is determined by experiments, then the invariant velocity can be taken as one of the general invariant velocity achieved in this Letter, then all results of current physical theories are consistent by utilizing this Letters theory.
Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-abelian Chern-Simons topological term in 2+1 dimensions, and use consistency of a gauge condition na
turally to deduce another gauge condition. Further, we get the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum has the orbital angular momentum and spin angular momentum of the non-abelian gauge field. Finally, we find out the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and the A_0^s (x) charge.
According to the method of path integral quantization for the canonical constrained system in Faddeev-Senjanovic scheme, we quantize the supersymmetrical electrodynamic system in general situation, and obtain the generating functional of Green functi
on. Another first class constraint is obtained by making the linear combination of several primary constraints, the generator of gauge transformation is constructed, gauge transformations of the all different fields are deduced. Utilizing the consistency equation of gauge fixing condition we deduce another gauge fixing condition, and we find that the secondary constraint of the system is an Euler-Lagrange equation that is just electro-charge conversation law. Thus, we do not need to calculate the other secondary constraints step by step, and get no new constraints naturally. So, the Faddeev-Senjanovic path integral quantization of the supersymmetrical electrodynamical system is simplified.
We give a general $SU(2)_Ltimes SU(2)_R$ $times U(1)_{EM}$ sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that $sigma $ and $pi ^0$ without
electric charges have electromagnetic interaction effects coming from their internal structure. A general Lorentz transformation relative to external sources $J_{gauge}$ $=(J_{A_mu},J_{A_mu ^kappa})$ is derived, using the general Lorentz transformation and the four-dimensional current of nuclear matter of the ground state with $J_{gauge}$ = 0, we give the four-dimensional general relations between the different currents of nuclear matter systems with $J_{gauge} eq 0$ and those with $J_{gauge}=0$. The relation of the densitys coupling with external magnetic field is derived, which conforms well to dense nuclear matter in a strong magnetic field. We show different condensed effects in strong interaction about fermions and antifermions, and give the concrete scalar and pseudoscalar condensed expressions of $sigma_0$ and $pi_0$ bosons. About different dynamical breaking and spontaneous vacuum symmetry breaking, the concrete expressions of different mass spectra are obtained in field theory. This paper acquires the running spontaneous vacuum breaking value $sigma_0^{prime},$ and obtains the spontaneous vacuum breaking in terms of the running $sigma_0^{prime}$, which make nucleon, $sigma $ and $pi $ particles gain effective masses. We achieve both the effect of external sources and nonvanishing value of the condensed scalar and pseudoscalar paticles. It is deduced that the masses of nucleons, $sigma $ and $pi $ generally depend on different external sources.
We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ) generalized brackets of the gauge invariant self-dual fields interacting with gauge fields. We further give FJ quantization of this system. Furthermore, the FJ method is com
pared with Dirac method, the results show the two methods are equivalent in the quantization of this system. And by the practical research in this letter, it can be found that the FJ method is really simpler than the Dirac method, namely, the FJ method obviates the need to distinguish primary and secondary constraints and first- and second-class constraints. Therefore, the FJ method is a more economical and effective method of quantization.
This paper uses the relation of the cosmic scale factor and scalar field to solve Wheeler-DeWitt equation, gives the tunnel effect of the cosmic scale factor a and quantum potential well of scalar field, and makes it fit with the physics of cosmic qu
antum birth. By solving Wheeler-DeWitt equation we achieve a general probability distribution of the cosmic birth, and give the analysis of cosmic quantum birth.
