Modified Born-Jordan Method For Constructing The Commutation Relation Of Coordinate and Momentum

The Born-Jordan method for constructing the quantum condition of the Matrix Mechanics is pointed out to be inappropriate in the present work. We modify this method and reconstruct the quantum condition by setting up a new expression for the Bohr quantum condition with the help of the (n,n) elements of the matrix $\oint\hat{p}(t){\rm d}\hat{x}(t)$

Some inequalities and limit theorems under sublinear expectations

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob's inequality for submartingale and Kolmogrov's inequality. By Kolmogrov's inequality, we obtain a special version of Kolmogrov's law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.Comment: 15 page

Initial-Final State Subspace of the SU(n) Gauge Theory with Explicit Gauge Field Mass Term

As a part of our study on the SU(n) gauge theory with explicit gauge field mass term this paper is devoted to form the Gupta-Bleuler subspace of the initial-final states in the scattering process.Comment: 4pages, rewritte

Approximate quantum state reconstruction without a quantum channel

We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to arbitrary number of users is generated at each port by ensemble of known quantum states with assistance of classical information of measurement outcomes by broadcasting. The obtained quantum state for each user is optimal in the sense that the fidelity universally achieves the upper bound. We present the universal quantum state distribution by providing physical realizable measurement bases in the cloud as well as the reconstruction method for each user. The quantum state reconstruction scheme works for arbitrary many identical pure input states in general dimensional system.Comment: 7 pages, 1 figur

An improvement on RPA based on a Boson mapping

We use a solvable model to perform modified dyson mapping and reveal the unphysical-state effects in the original Random Phase Approximation (RPA). We then propose a method to introduce the RPA and improve it based on a Boson mapping

Biharmonic maps from tori into a 2-sphere

Biharmonic maps are generalizations of harmonic maps. A well-known result of Eells and Wood on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere (whatever the metrics chosen) in the homotopy class of maps of Brower degree $\pm 1$. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. In this paper, we obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. Our results show that there exists no proper biharmonic maps of degree $\pm 1$ in a large family of maps from a torus into a sphere.Comment: 20 page

Renormalisability of the SU(n) Gauge Theory with Massive Gauge Bosons

The problem of renormalisability of the SU(n) theory with massive gauge bosons is reinverstigated in the present work. We expound that the quantization under the Lorentz condition caused by the mass term of the gauge fields leads to a ghost action which is the same as that of the usual SU(n) Yang-Mills theory in the Landau gauge. Furthermore, we clarify that the mass term of the gauge fields cause no additional complexity to the Slavnov-Taylor identity of the generating functional for the regular vertex functions and does not change the equations satisfied by the divergent part of this generating functional. Finally, we prove that the renormalisability of the theory can be deduced from the renormalisability of the Yang-Mills theory.Comment: 16 pages in Latex, no figures, Sections 3 and 4 were modifie

Renormalisability of the SU(2)×\timesU(1) Electroweak Theory with Massive W Z Fields and Massive Matter Fields

We extend the previous work and study the renormalisability of the SU$_L$(2) $\times$ U$_Y$(1) electroweak theory with massive W Z fields and massive matter fields. We expound that with the constraint conditions caused by the W Z mass term and the additional condition chosen by us we can still performed the quantization in the same way as before. We also show that when the $\delta-$ functions appearing in the path integral of the Green functions and representing the constraint conditions are rewritten as Fourier integrals with Lagrange multipliers $\lambda_a$ and $\lambda_y$, the total effective action consisting of the Lagrange multipliers, ghost fields and the original fields is BRST invariant. Furthermore, with the help of the the renormalisability of the theory without the the mass term of matter fields, we find the general form of the divergent part of the generating functional for the regular vertex functions and prove the renormalisability of the theory with the mass terms of the W Z fields and the matter fields.Comment: 21 pages, Latex, no figure

Biharmonic maps from a 2-sphere

Motivated by the rich theory of harmonic maps from a 2-sphere, we study biharmonic maps from a 2-sphere in this paper. We first derive biharmonic equation for rotationally symmetric maps between rotationally symmetric 2-manifolds. We then apply the equation to obtain a classification of biharmonic maps in a family of rotationally symmetric maps between 2-spheres. We also find many examples of proper biharmonic maps defined locally on a 2-sphere. Our results seem to suggest that any biharmonic map $S^2\longrightarrow (N^n, h)$ be a weakly conformal immersion.Comment: 18 page

One possible explanation for earthquake occurrences from anomalous line-of-sight propagations in the very high frequency band by fast Fourier transform spectral analysis

This paper illustrated the possible relationship between the occurrences of the earthquake and the anomalous line-of-sight propagations in the very high frequency band by the fast Fourier transform spectral analysis. Despite many anomalous propagations appear in the different very high frequency band during the earthquake occurrences, the majority of these abnormal signals contain similar frequency distributions in the frequency domain. For the 31 anomalous propagation spectral distributions, 30 of them present the same curve peaks, within a frequency range of (0-0.5)Hz. Furthermore, for the first time, we found that the spectral maximum of all anomalous propagations are below the characteristic Brunt-Vaisala frequency (period T larger than 6 min), which happens to be the frequency range of the internal gravity waves, which might evidence that the atmospheric gravity waves should be responsible for the indirect coupling between lithosphere and ionosphere. These novel results might provide direct evidence to the relationship between the anomalous propagations in the very high frequency band and the occurrences of earthquakes