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21.
Using two different types of the laddering equations realized simultaneously by the associated Gegenbauer functions, we show that all quantum states corresponding to the motion of a free particle on AdS
2 and S
2 are splitted into infinite direct sums of infinite-and finite-dimensional Hilbert subspaces which represent Lie algebras u(1, 1) and u(2) with infinite- and finite-fold degeneracies, respectively. In addition, it is shown that the representation bases of Lie algebras with rank 1, i.e., gl(2, C), realize the representation of nonunitary parasupersymmetry algebra of arbitrary order. The realization of the representation of parasupersymmetry algebra by the Hilbert subspaces which describe the motion of a free particle on AdS
2 and S
2 with the dynamical symmetry groups U(1, 1) and U(2) are concluded as well. 相似文献
22.
Myron W. Evans 《Foundations of Physics Letters》2003,16(6):513-547
A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group. 相似文献
23.
For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
24.
This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron
star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation
that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance
for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results
are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type)
magneto-elastic perturbation modes. 相似文献
25.
Blundell Tom L. Bolanos-Garcia Victor Chirgadze Dimitri Y. Harmer Nicholas J. Lo Thomas Pellegrini Luca Sibanda B. Lynn 《Structural chemistry》2002,13(3-4):405-412
Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site. 相似文献
26.
27.
关于由衍射片的背面反射光形成的衍射图样的讨论 总被引:1,自引:0,他引:1
在光的衍射实验中,我们看到的一般是由通过衍射片的直射光形成的衍射图样,但在衍射片的另一面,同样存在着另一个衍射图样,它是由衍射片的背面反射光形成的,两个衍射图样关于衍射片对称.本文给出了这种实验现象,并用巴比涅原理解释了这种现象. 相似文献
28.
DING Ning FANG Jian-Hui 《理论物理通讯》2006,46(2):265-268
In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained. 相似文献
29.
场源基本微元的对称性与场的性质 总被引:1,自引:1,他引:0
直接由标量基本微元(点源)和矢量基本微元(电流元等)的对称性和两个基本假设讨论基本微元产生的场矢量的性质。 相似文献
30.
A. Samokhin 《Acta Appl Math》2002,72(1-2):87-99