Magnetic monopoles in gauge theories

Magnetic monopoles in gauge theories are investigated. Let G be the gauge group and H the group of symmetries which are not spontaneously broken. The existence of magnetic monopoles is proved in the case when the group G has a compact covering group but the covering group of H is non-compact.     

Universal Groups of Effect Spaces

Various axiomatic models for unsharp quantum measurements are investigated. These include effect spaces (E-spaces), effect test spaces (E-test spaces), effect algebras, and test groups. It is shown that a test group G is the universal group of an E-test space if and only if G is strongly atomistic. It follows that if G is strongly atomistic, then G is an interpolation group. We then demonstrate that if G is an interpolation group, then G is the universal group of an E-space. Finally, it is shown that an E-space is isomorphic to an E-test space if and only if it is strongly atomistic.     

Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II

The extended Schwinger quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold M is a homogeneous Riemannian space with the given action of an isometry transformation group. Using the identification of M with the quotient space G/H, where H is the isotropy group of an arbitrary fixed point of M, we show that quantum mechanics on G/H possesses a gauge structure, described by a gauge potential that is the connection 1-form of the principal fiber bundle G(G/H, H). The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of the states are developed. Received: 27 June 2000 / Revised version: 10 May 2001 / Published online: 19 July 2001     

低频随机振动和正弦振动对汉语清晰度的影响

目的：探索随机振动和正弦振动因素下生成语音在听觉效果上的变化规律。方法：随机振动采用频率范围2-20Hz,加速度为0.3G、0.5G、0.7G(有效值,下同）,正弦振动采用频率4、6、8、10、12Hz,加速度为0.3G、0.5G;在安静及信噪比分别为0dB和-6dB三种状态下对随机振动组、正弦振组及对照组3个组的语音材料进行清晰度测试。结果：和对照组相比,随机振动组,清晰度几科没有变化,正弦振动组,0.3G时4Hz、0.5G时6Hz和8Hz作用下语音清晰度有明显降低,检验结果非常显著。研究还发现,清晰度的降低随听音环境的信噪比的降低而变得严重;结论：正弦振动对发音人发音的影响,会使通话效果变差,并且在听音环境恶劣时尤为突出。     

Representations of the infinite direct product of universal coverings of isometry groups of the complex ball

In this paper we consider the group G?_M consisting of measurable functions on the set M with values in the group G? which is the universal covering of the group G of isometries of the n-dimensional complex ball. We construct a family of irreducible unitary representations of this group. The main elements of the construction are irreducible representations of the group G? obtained by interpolation from the representations of the discrete series of the group G.Suppose G? is a group, M a set with measure. Denote by G?_M the group of G?-valued functions on M. (The group G?_M does not necessarily contain all the functions). It is natural to consider the group G?_M as the direct product of ? copies of the group G?, where ? is the cardinality of the set M. In the case where the set M has no points of non-zero measure, it is natural to call G?_M the continuous tensor product of ? copies of G?. In the case where G? is the Heisenberg–Weyl group $\text{1}\text{a}\text{c}\text{0}\text{1}\text{b}\text{0}\text{0}\text{1}$ the group G?_M has been known since the end of the 1920, in view of the fact that the Lie algebra of this group is the Lie algebra of the Bose commutation relations.¹ The case where the group G? is semi-simple apparently first occurred in the theory ofcalibrated fields. A number of physical and mathematical papers (see [1], [2], [8]–[11]) are concerned with the groups G?_M and their linear representations. The present paper deals with the case where the group G? is the universal covering of the isometry group G of the complex ball (i.e. the domain in Cⁿ determined by the inequality ∑ z_kz?_k < 1). No conditions are imposed on the set M. By comparison with the papers [1], [2], [8]–[10], the explicit construction of the representations, copying the Fock representation, is new, as well as the proof of their irreducibility.The construction proposed below may be generalized to the case where G is the isometry group of any homogeneous domain Ω in Cⁿ, G? is the one-dimensional central extension of G. However, if Ω is a classical symmetrical domain (which is not a ball) and the set M contains no points of non-zero measure, it follows from [6] that the representation thus obtained is unitary in the indefinite sense. In the case where Ω = Cⁿ and G is the group of parallel translations G?—the Heisenberg-Weyl group, the proposed construction becomes the Fock construction of the representation of commutation relations. The other cases have not been studied yet. The main results of this paper have been (briefly) published in [4].     

Results on BRS cohomologies in gauge theory

We compute the cohomology of the Becchi-Rouet-Stora operator in gauge theory over general space-time M without boundary, with structure group G, for class of polynomial functions of the field. We show that the problem reduces to a standard problem for the finite dimensional group G. As a consequence, we prove that, within this class of polynomials, all anomalies and Schwinger terms are obtained from invariants of G.     

空间群O_h~7O~4T~2母分系数的计算

在群链G G_1 G_2中,把两个子群的IR(不可约表示)基相乘,然后把乘积基耦合成IR基,耦合系数我们称之为母分系数。本文把陈金全创立的本征函数法用于计算空间群的群链O_h~7 O~4 T~2的母分系数,计算的结果显示母分系数是满足正交关系,同时也说明此方法是适用的。     

On the complete integrability of the static axially symmetric self-dual gauge field equations for an arbitrary group

We present an analysis of static axially symmetric gauge fields for an arbitrary gauge group G. Two ansätze are considered. The full ansatz involves a total of 4d(d = dim G), the reduced ansatz only 2d functions of (?, z). Imposing self-duality is shown to reduce the problem to a sigma model in the curved two-dimensional (?, z) space over the coset spaces G?/G for the full, and G¹/K for the reduced ansatz. G? is the complexification of G. ¹ is a particular non-compact form of G, and K the local form-preserving symmetry group of the reduced ansatz. We give explicitly the Lax-pair type representations (linear scattering problem) of the sigma model, indicating that the standard methods available for certain non-linear two-dimensional problems can be used to generate solutions. Our procedure has the advantage that only real fields over a real manifold enter the analysis.     

Effects of self-fields on electron trajectory and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding

The effects of self-fields on electron trajectories and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding are investigated. An analysis of the two-stream quasi-steady-state electron trajectories is given by solving the equation of motion in the presence of ion-channel guiding and the planar wiggler. The electron trajectories and the gain are derived. The stability of the trajectories, the characteristics of the linear gain, and the normalized maximum gain are studied numerically. The numerical calculations show that there are eight group trajectories rather than the two groups reported in the absence of the self-fields. It is also shown that the normalized gain group seven （G7） decreases while the rest increases with the increase in normalized ion-channel frequency. The two-stream instability and the self-field lead to a decrease in the maximum gain, except for G7.     

Global symmetries in four and higher dimensions

Knowing that a four-dimensional theory with gauge group G₀ is unified in theory with gauge group G puts restrictions on what global symmetries are possible in the low-energy world. Here we analyze those restrictions assuming that unification in G occurs inn four dimensions and assuming that unification occurs only in a higher-dimensional theory. There are possibilities for global symmetries which are not possible in the former case, so in principle indirect evidence for higher dimensions might be found by finding peculiar global symmetries in the low-energy world.     

Symmetry analysis of magnetic structures and spin-waves on the basis of a stabilizer concept

The common scheme for the group theory analysis of a crystal magnetic structure and a spin-wave spectrum is developed. This scheme is based on the representation theory of a crystal space group G (for magnetic structure analysis) and on the co-representation theory of the Shubnikov group M of a magnetically ordered crystal (for spin wave analysis).Unlike the standard calculation, the procedure proposed in this paper is based on the conception of the stabilizer-the symmetry group of single atoms, and this considerably symplified the calculation work, reducing it to the work with the elements of the stabilizer and with the representatives of the expansion of the G or M groups with respect to the group of the stabilizer. It is enough to calculate the components of the basic functions only at one atom, as for the other atoms they may be found by the action of the representatives.For the symmetrization of the spin wave Hamiltonian matrix a new mathematical procedure is used the expansion of group G over the double coset classes. It lets us easily find the symmetric relations between the different matrix elements. The method is illustrated in the example of the complicated magnetic structure of a garnet Dy₃Al₅O₁₂. The advantages of the new method are especially obvious in the case of structures with a great number of magnetic atoms in a primitive cell.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct the lattice formulation of the pure gauge fields in a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a fourdimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the quark system by calculating latt-ice current-current propagztor when the coset pure gauge fields are retained manifest1y.     

简立方结构磁空间群耦合系数计算

利用本征函数法（EFM方法）计算了Oh^1结构磁空间群第一布里渊区部分点的C－G系数。     

On the support of Plancherel measure

Let G be a real reductive group. As follows from Plancherel formula for G, proved by Harish-Chandra, only tempered representations of G contribute to the decomposition of the regular representation in L²(G). We give a simple direct proof of this result, based on Gelfand-Kostyuchenko method. We also prove similar results for representations, which appear in the decomposition of L²(X), where X is a homogeneous G-space of polynomial growth. (See precise definition in 3.5). Important examples of such space X are semisimple symmetric spaces and quotient of G by arithmetic subgroups.     

二十面体群C-G系数计算

本文简要介绍了计算Ｃ Ｇ系数的生群元矩阵方程法，给出计算二十面体群Ｃ Ｇ系数时采用的简化计算方法，并给出了Ⅰ群Ｃ Ｇ系数的计算结果。     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

Self-dual monopoles and toda molecules

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.     

Group mobility assisted network selection framework in 5G vehicular cognitive radio networks

The heterogeneity nature of networks is the most eminent characteristic in 5G vehicular cognitive radio networks across complex radio environments. Since multiple communicating radios may be in motion at the same time in a vehicle. So, group mobility is the most prominent characteristic that requires to be a deep investigation. Therefore, different communication radios that are moving on a train/bus needed to select the networks simultaneously. Without considering the group mobility feature, there is a possibility that the same network may be selected by each moving node and cause congestion in a particular network. To overcome this problem, a novel network selection technique considering the group mobility feature is proposed to improve the throughput of the network. In this work, a 5G vehicular cognitive radio network scenario is also realized using USRP-2954 and LabVIEW communications system design suite testbed. The performance metrics like transmission delay, packet loss rate, reject rate and, channel utilization for vehicular nodes, are gained to analyze the proposed technique in vehicular cognitive radio networks environment. The proposed technique demonstrates a remarkable improvement in channel utilization for vehicular nodes and outperformed conventional schemes.     

Automorphisms of orthomodular lattices and symmetries of quantum logics

Given a group G, there is a proper class of pairwise nonembeddable orthomodular lattices with the automorphism group isomorphic to G. While the validity of the above statement depends on the used set theory, the analogous statement for groups of symmetries of quantum logics is valid absolutely.