Massive Gauge Bosons in Yang-Mills Theory without Higgs Mechanism

Two kinds of Yang-Mills fields are found upon the concepts of mass eigenstate and nonmass eigenstate. The Yang-Mills fields of the first kind were proposed by Yang and Mills, which couple to the mass eigenstates with the same rest mass, whose gauge bosons are massless. I find that there are second kind of Yang-Mills fields, which are constructed on a five-dimensional manifold. Only the nonmass eigenstates couple to the Yang-Mills fields of the second kind, which are the nonmass eigenstates as well and composed of mass eigenstates of gauge bosons. The mass eigenstates of the Yang-Mills fields of the second kind live in the four-dimensional spacetime, the corresponding gauge bosons of which may be massive. The SU(2)\times U(1) gauge fields of the second kind are studied carefully, whose gauge bosons, which are the mass eigenstates, are the W^{\pm}, Z^{0} and photon fields. The rest masses of W^{\pm} and Z^{0} obtained are the same as that given by the Glashow-Salam-Weinberg model of electroweak interactions. It is discussed that this model should be renormalizable.Comment: 14 page

Right-handed Neutrino Fields are Real Spinors

The ansatz that the right-handed neutrino fields are real spinors is proposed in this letter. We naturally explain why the right-handed neutrinos don't feel the electroweak interactions and why there is neutrino mixing. It is found that the Majorana representation of Dirac equation is uniquely permitted in our scenario. With this ansatz, we predict that: 1. there are at least four species of neutrinos; 2. the mass matrix of neutrinos must be traceless; 3. there is CP violation in the lepton sector. The difference between our scenario and the Zee model is discussed also.Comment: 4 pages, no figure

Massive Gauge Bosons in Yang-Mills Theory without Higgs Mechanism

A new mechanism giving the massive gauge bosons in Yang-Mills theory is proposed in this letter. The masses of intermediate vector bosons can be automatically given without introducing Higgs scalar boson. Furthermore the relation between the masses of bosons and the fermion mass matrix is obtained. It is discussed that the theory should be renormalizable.Comment: 4 pages, Latex, no figur

Nonmass Eigenstates of Fermion and Boson Fields

It appears natural to consider the four dimensional relativistic massive field as a five dimensional massless field. If the fifth coordinate is interpreted as the proper time, then the fifth moment can be understood as the rest mass. After introducing the rest mass operator, we define the mass eigenstate and the nonmass eigenstate. The general equations of spin 0, spin 1/2 and spin 1 fields are obtained respectively. It is shown that the Klein-Gordon equation, the Dirac equation and the Proca equation describe the mass eigenstates only. The rest mass of spin 1/2 field and the rest mass squared of Boson fields are calculated. The U(1) gauge field that couples to the nonmass eigenstates is studied carefully, whose gauge boson can be massive.Comment: 13 pages, the rest mass operator is revise

Special-series solution of the first-order linear vector differential equation

A special series is introduced in this paper to yield solution of the first-order linear vector differential equation. It is proved that if the differential equation satisfied by the first term of this series can be solved exactly, then other terms can be determined by the method of variation of parameters. We point out that the special series will be the solution of the first-order linear vector differential equation if the infinite special series converges. An illustrative example has been given to outline the procedure of our method.Comment: 14 pages, no figures, submitted to J.Differential Equation

Unification of Gravitation and Gauge Fields

In this letter, I indicate that complex daor field should also have spinor suffixes. The gravitation and gauge fields are unified under the framework of daor field. I acquire the elegant coupling equation of gravitation and gauge fields, from which Einstein's gravitational equation can be deduced.Comment: 7 pages, the second letter on daor fiel

Covariant Theory of Gravitation in the Spacetime with Finsler Structure

The theory of gravitation in the spacetime with Finsler structure is constructed. It is shown that the theory keeps general covariance. Such theory reduces to Einstein's general relativity when the Finsler structure is Riemannian. Therefore, this covariant theory of gravitation is an elegant realization of Einstein's thoughts on gravitation in the spacetime with Finsler structure.Comment: 18 pages, no figur

Exact solutions of the Dirac equation in Robertson-Walker space-time

The covariant Dirac equation in Robertson-Walker space-time is studied under the comoving coordinates. The exact forms of the spatial factor of wave function are respectively acquired in closed, spatially flat, and open universes.Comment: 10 page

Adaptive estimation of the rank of the coefficient matrix in high dimensional multivariate response regression models

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the one proposed in Bunea, She and Wegkamp [7] in that it does not require estimation of the unknown variance of the noise, nor depends on a delicate choice of a tuning parameter. We develop an iterative, fully data-driven procedure, that adapts to the optimal signal to noise ratio. This procedure finds the true rank in a few steps with overwhelming probability. At each step, our estimate increases, while at the same time it does not exceed the true rank. Our finite sample results hold for any sample size and any dimension, even when the number of responses and of covariates grow much faster than the number of observations. We perform an extensive simulation study that confirms our theoretical findings. The new method performs better and more stable than that in [7] in both low- and high-dimensional settings

Testing for pure-jump processes for high-frequency data

Pure-jump processes have been increasingly popular in modeling high-frequency financial data, partially due to their versatility and flexibility. In the meantime, several statistical tests have been proposed in the literature to check the validity of using pure-jump models. However, these tests suffer from several drawbacks, such as requiring rather stringent conditions and having slow rates of convergence. In this paper, we propose a different test to check whether the underlying process of high-frequency data can be modeled by a pure-jump process. The new test is based on the realized characteristic function, and enjoys a much faster convergence rate of order $O(n^{1/2})$ (where $n$ is the sample size) versus the usual $o(n^{1/4})$ available for existing tests; it is applicable much more generally than previous tests; for example, it is robust to jumps of infinite variation and flexible modeling of the diffusion component. Simulation studies justify our findings and the test is also applied to some real high-frequency financial data.Comment: Published at http://dx.doi.org/10.1214/14-AOS1298 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org