Decomposition of Noncommutative U（1） Gauge Potential

We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor     

Quantum electrodynamics with arbitrary charge on a noncommutative space

Using the Seiberg-Witten map, we obtain a quantum electrodynamics on a noncommutative space, which has arbitrary charge and keep the gauge invariance to at the leading order in theta. The one-loop divergence and Compton scattering are reinvestigated. The noncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics.     

Quantum electrodynamics with arbitrary charge on a noncommutative space

Using the Seiberg-Witten map,we obtain a quantum electrodynamics on a noncommutative space,which has arbitrary charge and keep the gauge invariance to at the leading order in theta.The one-loop divergence and Compton scattering are reinvestigated.The uoncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics.     

Noncommutative gauge fields coupled to noncommutative gravity

We present a noncommutative (NC) version of the action for vielbein gravity coupled to gauge fields. Noncommutativity is encoded in a twisted $\star $ -product between forms, with a set of commuting background vector fields defining the (abelian) twist. A first order action for the gauge fields avoids the use of the Hodge dual. The NC action is invariant under diffeomorphisms and $\star $ -gauge transformations. The Seiberg–Witten map, adapted to our geometric setting and generalized for an arbitrary abelian twist, allows to re-express the NC action in terms of classical fields: the result is a deformed action, invariant under diffeomorphisms and usual gauge transformations. This deformed action is a particular higher derivative extension of the Einstein-Hilbert action coupled to Yang-Mills fields, and to the background vector fields defining the twist. Here noncommutativity of the original NC action dictates the precise form of this extension. We explicitly compute the first order correction in the NC parameter of the deformed action, and find that it is proportional to cubic products of the gauge field strength and to the symmetric anomaly tensor $D_{IJK}$ .     

Projection Operator on Rational Noncommutative OrbifoldT2/Z4

In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator \hat{P} on the rational noncommutative orbifold T²/Z₄. we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.     

U(1) gauge field theory on κ-Minkowski space

This study of U(1) gauge field theory on the kappa-deformed Minkowski space-time extends previous work on gauge field theories on this type of noncommutative space-time.We construct the conserved gauge current, fix part of the ambiguities in the Seiberg-Witten map and obtain an effective U(1) action invariant under the action of the undeformed Poincare group. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Nonperturbative dynamics of noncommutative gauge theory

We present a nonperturbative lattice formulation of noncommutative Yang–Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with p·n_f flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n_f species of matter on a lattice of size p·L with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.     

Approximate wø ∽ Ωø Relations in Quintessence Models

Quintessence field is a widely-studied candidate of dark energy. There is ``tracker solution' in quintessence models, in which evolution of the field ø at present times is not sensitive to its initial conditions. When the energy density of dark energy is neglectable (Ω<sub>ø</sub><< 1), evolution of the tracker solutioncan be well analysed from ``tracker equation'. In this paper, we try tostudy evolution of the quintessence field from ``full tracker equation',which is valid for all spans of Ω<sub>ø.</sub> We get stable fixed points of w<sub>ø</sub> and Ω<sub>ø</sub> (noted as \hat{w}<sub>ø</sub> and \hat{Ω}<sub>ø</sub>) from the ``full tracker equation', i.e., w_ø and Ω_ø will always approach \hat{w}_ø and \hat{Ω}_ø respectively. Since \hat{w}_ø and \hat{Ω}_ø are analytic functions of ø, analytic relation of \hat{w}_ø ~ \hat{Ω}_ø can be obtained, which is a good approximation for the w_ø ~ Ω_ø relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities \hat{w}_ø < w_ø and \hat{Ω}_ø < Ω_ø are statisfied if the w_ø (or \hat{w}_ø) decreases with time. In this way, the potential U(ø) can be constrained directly from observations, by no need of solving the equations of motion numerically.     

Thermodynamics of a Charged Particle in a Noncommutative Plane in a Background Magnetic Field

Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used to map the noncommutative system to its commutative equivalent system. In particular we have computed the partition function of the system and from this we obtained the susceptibility of the Landau system and found that the result gets modified by the spatial noncommutative parameter θ. We also investigate the de Hass–van Alphen effect in noncommutative space and observe that the oscillation of the magnetization and the susceptibility gets noncommutative corrections. Interestingly, the susceptibility in the noncommutative scenario is non-zero in the range of the magnetic field greater than the threshold value which is in contrast to its commutative counterpart. The results obtained are valid upto all orders in the noncommutative parameter θ.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.     

Inconsistencies of the U(1) Theory of Electrodynamics: Stress Energy Momentum Tensor

The internal gauge space of electrodynamics considered as a U(1) gauge field theory is a scalar. This leads to the result that in free space, and for plane waves, the Poynting vector and energy vanish. This result is consistent with the fact that U(1) gauge field theory results in a null third Stokes parameter, meaning again that the field energy vanishes in free space. A self consistent definition of the stress energy momentum tensor is obtained with a Yang Mills theory applied with an O(3) symmetry internal gauge space. This theory produces the third Stokes parameter self consistently in terms of the self-dual Evans-Vigier fields B(3).     

自由质点测地线仿射参量时空坐标系

以时序t为自变量,可给出自由质点空间测地线的参数方程组{Xⁱ(t)},借助于仿射参量R(t)变换实现测地线微分方程的齐次化, 推导出仿射参量R满足的一阶微分方程、获得以有理数C_u为标志的序列解析解R.基于R定义平直四维坐标系{t,r,θ,φ}的空间距离单位,建立自由质点测地线仿射参量时空坐标系{t,ξ,θ,φ}.研究{t,ξ,θ,φ}中狭义相对论时空间隔模型度规张量g的对角化过程, 发现与对角化度规对应的特征量t₁(t,ξ), τ₁(τ,ξ),t_t(t,τ,ξ),τ_τ1(t,τ,ξ); 从而推出时空坐标系{t,ξ,θ,φ}维数小于4.     

Noncommutative induced gauge theory

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang–Mills-type effective theory generated from the integration over the scalar field. We find that the gauge-invariant effective action involves, beyond the expected noncommutative version of the pure Yang–Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative ϕ⁴-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.     

Higgs signal in chargino-neutralino production at the LHC

We have analyzed the prospect of detecting a Higgs signal in mSUGRA/cMSSM based Supersymmetric (SUSY) model via chargino-neutralino ( ${\tilde{\chi}}^{\pm}_{1}\tilde{\chi}^{0}_{2}In order to generate mass for an abelian spin-1 vector field while preserving gauge invariance we couple it to a symmetric tensor. The derivative coupling includes up to three derivatives. We show that unitarity, causality and absence of Stueckelberg (compensating) fields single out a unique model up to trivial field redefinitions. The model contains one massive and one massless spin-1 particle. It is shown by means of a master action to be dual to the direct sum of a Maxwell plus a Maxwell?CProca theory.     

Noncommutative products of Euclidean spaces

We present natural families of coordinate algebras on noncommutative products of Euclidean spaces \({\mathbb {R}}^{N_1} \times _{\mathcal {R}} {\mathbb {R}}^{N_2}\). These coordinate algebras are quadratic ones associated with an \(\mathcal {R}\)-matrix which is involutive and satisfies the Yang–Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces \({\mathbb {R}}^{4} \times _{\mathcal {R}} {\mathbb {R}}^{4}\). Among these, particularly well behaved ones have deformation parameter \(\mathbf{u} \in {\mathbb {S}}^2\). Quotients include seven spheres \({\mathbb {S}}^{7}_\mathbf{u}\) as well as noncommutative quaternionic tori \({\mathbb {T}}^{{\mathbb {H}}}_\mathbf{u} = {\mathbb {S}}^3 \times _\mathbf{u} {\mathbb {S}}^3\). There is invariance for an action of \({{\mathrm{SU}}}(2) \times {{\mathrm{SU}}}(2)\) on the torus \({\mathbb {T}}^{{\mathbb {H}}}_\mathbf{u}\) in parallel with the action of \(\mathrm{U}(1) \times \mathrm{U}(1)\) on a ‘complex’ noncommutative torus \({\mathbb {T}}^2_\theta \) which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.     

Towards a $$Z\prime $$ Gauge Boson in Noncommutative Geometry

We study all possible U(1)-extensions of the standard model within the framework of noncommutative geometry with the algebra . Comparison to experimental data about the mass of a hypothetical gauge boson leads to the necessity of introducing at least one new family of heavy fermions.     

SO(n)规范势的可分解理论

使用几何代数方法,研究了n维紧致黎曼流形上SO(n)规范势(自旋联络)的一般分解理论,建立了SO(n)规范场用球丛上单位矢量场n分解的一般表达式.由此,分别得到了U(1)规范场和U(2)规范场用单位矢量场n分解的一般形式.     

Muon anomaly and dark parity violation

The muon anomalous magnetic moment exhibits a 3.6σ discrepancy between experiment and theory. One explanation requires the existence of a light vector boson, Z_{d} (the dark Z), with mass 10-500?MeV that couples weakly to the electromagnetic current through kinetic mixing. Support for such a solution also comes from astrophysics conjectures regarding the utility of a U(1)_{d} gauge symmetry in the dark matter sector. In that scenario, we show that mass mixing between the Z_{d} and ordinary Z boson introduces a new source of "dark" parity violation, which is potentially observable in atomic and polarized electron scattering experiments. Restrictive bounds on the mixing (m_{Z_{d}}/m_{Z})δ are found from existing atomic parity violation results, δ^{2}<2×10^{-5}. Combined with future planned and proposed polarized electron scattering experiments, a sensitivity of δ^{2}～10^{-6} is expected to be reached, thereby complementing direct searches for the Z_{d} boson.