3,439 research outputs found
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
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 . 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 in a large family of
maps from a torus into a sphere.Comment: 20 page
Renormalisability of the SU(2)U(1) Electroweak Theory with Massive W Z Fields and Massive Matter Fields
We extend the previous work and study the renormalisability of the SU(2)
U(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
functions appearing in the path integral of the Green functions and
representing the constraint conditions are rewritten as Fourier integrals with
Lagrange multipliers and , 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
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
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
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
be a weakly conformal immersion.Comment: 18 page
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