The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field

Based on the opinion that the γ-matrices in Dirac equation have structure and are decomposable, we decompose the γ-matrices into the direct product of the operators in the spin space and the particle-antiparticle space. By using this method, we attain a complete set of commutative operators, a set of quantum numbers and the correspondingly eigen solutions of the Hamiltonian for a charged Dirac particle moving in a uniform constant magnetic field. In addition, the dynamic supersymmetry of the Hamiltonian is unveiled. Spin symmetry breaking and particle-antiparticle symmetry breaking are discussed, and the supersymmetric group operator of the degenerate spin subspace resulting from the spin residual supersymmetry is found.     

Large linear magnetoresistance in a new Dirac material BaMnBi_2

Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles.Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials.In this paper,we report the synthesis of high quality single crystals of BaMnBi_2 and investigate the transport properties of the samples.BaMnBi_2 is a metal with an antiferromagnetic transition at T_N = 288 K.The temperature dependence of magnetization displays different behavior from CaMnBi_2 and SrMnBi_2,which suggests the possible different magnetic structure of BaMnBi_2.The Hall data reveals electron-type carriers and a mobility μ(5K)= 1500 cm~2/V·s.Angle-dependent magnetoresistance reveals the quasi-two-dimensional(2D) Fermi surface in BaMnBi_2- A crossover from semiclassical MR~H~2dependence in low field to MR~H dependence in high field,which is attributed to the quantum limit of Dirac fermions,has been observed in magnetoresistance.Our results indicate the existence of Dirac fermions in BaMnBi_2.     

The mass-scale of supersymmetry breaking and proton decay

A fundamental mass-scale is associated with the transition of supersymmetric SU(3)_c×SU(2)_L×U(1) to the ordinary SU(3)_c×SU(2)_L×U(1) symmetry of elementary particle interactions. The renormalisation of the gauge coupling in a supersymmetric SU(5) grand unification leads to the mass-scale of supersymmetry breaking to be of order 10¹² GeV if the lifetime of the proton is taken to be 10³⁰ y and is lowered to the mass-scale of ordinary electroweak interactions if the proton lives longer than 10³⁰ y. It is lower than 10¹² GeV if the contribution of light scalars is taken into account. The predictions of the weak angle sin²θ (M_W) are in excellent agreement with experiment.     

STRING THEORY WITH THREE FAMILIES OF CHIRAL FERMIONS

A heterotic string theory is constructed by compactifying directly from 26 to 4 dimensions via a smooth manifold T²²/G. In the low energy limit, there are three families of chiral fermions with exactly the same quantum numbers as thatin the standard supersymmetric SU(3)×SU(2)×XU(1) model. They couple to supergravity and supergauge fields with the gauge symmetry SU(3)_F×SU(3)_c×SU(3)_L×U(1)_YR×U(1)_I3R.     

The Unitary Operator Corresponding to the General Two-Mode Coordinate-Momentum Mixed Transformation

We discuss the unitary operator corresponding to the general two-mode coordinate-momentum mixed transformation(q2,p2)→(Aq1 Bq2,Cq1 Dp2),where A,B,C and Dare arbitrary real numbers,Suitably selecting the parameters A,B,Cand D,we obtain a new two-mode bosonic realization of the SU(1,1) Lie algebra.We also study the squeezing effects of the squeezed vacuum associated with the new two-mode bosonic realization of the SU(1,1) Lie algebra.The results show that the new squeezed vacuum does not possess second-order squeezing,but exhibits higher-order squeezing.     

Quantenphysikalischer Ursprung der Eichidee

The Quantum Physical Origin of the Gauge Idea To consider quantum physics as an interplay of creation and annihilation processes has the consequence that gauge field theories are not only possible but necessary. Since the complex conjugate phase factors of each pair of fermion creators and annihilators can be arbitrary chosen, quantum field theories must be completely phase invariant. Unfortunately, even globally the Dirac equation for systems of free fermions is not phase invariant. The Dirac matrices are namely transformed, if we multiply the spinor components by different constant phase factors. The Dirac equations before and after the transformation are however physically equivalent. We may therefore say: Systems of free fermions will be completely described, only if we consider the class of all equivalent Dirac equations. Since Dirac's commutation relations are unitarily invariant, the class equivalent Dirac equations is invariant under all transformations of the group U 4. Unitary diagonal matrices yield arbitrary phase transformations. Hence, gauge fields of the group U 4 are compatible with the postulate of general phase invariance. These gauge file are so similar to the QED that we may speak of an “extended quantum electrodynamics”, EQE. Here, we will show that EQE exists. The invariant subgroup U 1 U 4 yields QED. The complementary subgroup SU 4 includes four subgroups SU 3, there subgroups O 4, and six subgroups SU 2. The latter ones may yield three pairs of quarks and three pairs of leptons, where the quarks form a group SU 3. More than two times three pairs of elementary fermions does not exist in in EQE Probably, EQE is different from the United EQD and QCD. However, it should be a promising version of a field theory in elementary particle physics, because it follows from an existing symmetry of the empirically wel founded Dirac theory. EQE is therefore free from hypothesis in the Newtonian sense of the word. Whatever it will finally mean, it cannot be rejected, since phase invariance must be required. The invention of new symmetries and the acception of a bie number of independent spinor components is dispensable or must be postponed at least.     

Supersymmetric left-right model and its tests in linear colliders

We investigate phenomenological implications of a supersymmetric left-right model based on SU(2)_L × SU(2)_R × U(1)_B–L gauge symmetry testable in the next generation linear colliders. We concentrate in particular on the doubly charged SU(2)_R triplet higgsino , which we find very suitable for experimental search. We estimate its production rate in e⁺e⁻, e⁻e⁻, e⁻γ and γγ collisions and consider its subsequent decays. These processes have a clear discovery signature with a very low background from other processes.     

Moduli Space of IIB Superstring and SUYM in AdS5 × S5

This paper consists of two parts. In part I, we interpret the hidden symmetry of the moduli space of IIB superstring on AdS₅×S⁵ in terms of the chiral embedding in AdS₅, which turns out to be the CP³ conformal affine Toda model. We review how the position μ of poles in the Riemann-Hilbert formulation of dressing transformation and the value of loop parameter μ in the vertex operator of affine algebra determine the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinizes the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients μ of twistor. In part II, by extending the dressing symmetric action of IIB string in AdS₅×S⁵ to the D₃ brane, we find a gauged WZW action of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structures of left and right α-planes glue into an ambitwistor. The symmetry group of Nahm equations is centrally extended to an affine group, thus we explain why the spectral curve is given by affine Toda.     

Symmetries of massless Dirac equations and supersymmetric quantum mechanics

It is shown how symmetries of Dirac equations can be used to obtain constants of motion for nonrelativistic supersymmetric quantum Hamiltonians. In particular, conserved supercharges are found for a spin-1/2 particle in the field of a dyon which yield under anticommutation the generalized Runge-Lenz symmetry of the system.This work is supported in part through funds provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Fonds FCAR of the Quebec Ministry of Education.     

Dirac粒子的正-反粒子自由度和正-反粒子量子数

对Dirac粒子引进了正 反粒子自由度和相应的内部τ空间的算子,把γ矩阵分解成自旋σ算子和正 反粒子τ算子;Dirac方程的解出现了正 反粒子量子数;正 反粒子变换是Dirac粒子的哈密顿量的反对称变换,Dirac粒子负能态能量的负值来自正 反粒子量子数的负值;γ矩阵这种分解是处理物理相互作用的需要. he particle-antiparticle degrees of freedom and the corresponding intrinsic space are introduced to study the dynamical symmetry of the Dirac particle. As a result, the particle-antiparticle quantum number appears naturally and the Dirac particle has five quantum numbers instead of four. An anti-symmetry of the Dirac Hamiltonian and a dual symmetry of its eigen functions are explored. The operator of the Dirac equation in central potentials is found to be the analog of the helicity operator of ...     

A symmetry reduction scheme of the Dirac algebra without dimensional defects

In relating the Dirac algebra to homogeneous coordinates of a projective geometry, we present a simple geometric scheme which allows to identify various Lie algebras and Lie groups well-known from classical physics as well as from quantum field theory. We introduce a 1 -point-compactification and quaternionic Möbius transformations, and we use SU* (4) and a symmetry reduction scheme without dimensional defects to identify transformations and particle representations thoroughly. As such, two subsequent nonlinear σ models SU*(4)/U Sp(4) and U Sp(4)/SU(2) × U(1) emerge as well as a possible double coset decomposition of SU*(4) with respect to SU(2) × U(1). Whereas the first model leads to equivalence classes of hyperbolic manifolds and naturally introduces coordinates and velocities, the second coset model leads to a Hermitian symmetric (vector) space (Kählerian space) of real dimension 6, i.e., to a 3-dimensional complex space with a global symplectic and a local SU(2) × U(1) symmetry which allows to identify the (local) gauge group of electroweak interactions as well as under certain assumptions it admits compact SU(3) transformations as automorphisms of this 3-dimensional (hyper)complex vector space. In the limit of low energies, this geometric SU*(4) scheme naturally yields the (compact) group SU(4) to describe “chiral symmetry” and conserved isospin of hadrons as well as the low-dimensional hadron representations. Last not least, with respect to some of the SU*(4) generators we find a multiplication table which (up to signs) is identical with the octonions represented in the Fano plane.     

Duality in Off-Shell Electromagnetism

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five-dimensional U(1) gauge theory associated with Stueckelberg–Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five-dimensional theory prevents a natural generaliza tion of the Dirac monopole, since the theory is not symmetric under duality transforma tions. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of a Clifford algebra. Nevertheless, the generalized framework does not permit us to recover the phenomenological (or conventional) absence of magnetic monopoles.     

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.     

Towards a finite N = 2 susy GUT

We consider finite, N = 2 supersymmetric GUTs based on gauge groups SU(n) and SO(n). As an example, we discuss a semirealistic model based on SO(12). We argue that in finite, N = 2 supersymmetric GUTs, gauge symmetry breaking should occur dynamically. We present a heuristic picture in which this is induced by soft, finiteness preserving SUSY breaking terms. The bound states formed cause a very rapid evolution of the SO(12) coupling constant and break SO(12) into SU(4)×SU(3)_C×U(1).     

A Secondary Operator Ordering Problem for a Charged Rigid PlanarRotator in Uniform Magnetic Field

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum pi(i= 1, 2, 3) in usual kinetic energy (1/2μ)∑Pi^2, and the correct kinetic energy turns out to be (1/2μ)∑(1/fi)pifipi, where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions f i is given for a charged rigid planar rotator in the uniform magnetic fieM.     

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p,χ₂,χ₃,χ₄〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p→e^λ₁p, χ₂→ e^λ₂χ₂, χ₃→e^λ₃χ₃, and χ₄→e^λ₄χ₄ in the state |p,χ₂ ,χ₃ ,χ₄〉is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.     

Symplectic Geometry,Hopf Algebraic Structures of Classical and Quantum q-Deformations of SU(2) Algebra

By deforming the symplectic structure on S², we get the q-deformation of SU(2) algebra at classical level, SU_q,h→0(2), in a Hamiltonian approach. Furthermore, we construct a set of operators on the line bundle over the deformed symplectic manifo1d.S_q² such that they form SU_q,h→0(2) in Lie brackets and set up a nontrivial Hopf algebra with a parameter q only in such a classical Hamiltonian system. We also show that the deformations from S_q² to S_q² are a set of quasiconformal transformations. The quantization via geometric approach of the system gives rise to the quantum q-deformed algebra SU_q,h(2), wnich has a Hopf algebraic structure with two independent parameters q and h.     

拓扑绝缘体(Bi0.5Sb0.5)2Te3薄膜中的线性磁阻

本文报道了拓扑绝缘体(Bi_0.5Sb_0.5)₂Te₃薄膜中线性磁阻问题的系统性研究工作. 此体系中, 线性磁阻在很宽的温度和磁场范围内出现: 磁场高达18 T时磁阻仍没有饱和趋势, 并且当温度不高于50 K时, 线性磁阻的大小对温度的变化不敏感. 栅压调控化学势可明显改变线性磁阻的大小. 当化学势接近狄拉克点时, 线性磁阻最为显著. 这些结果说明电荷分布的不均匀性是引起该材料线性磁阻的根源.     

q-Deformed U(5) Limit in s,d IBM for Nuclei

The q-deformed Hamiltonian with U(5) symmetry in s , d interacting boson model can be constructed by using quantum algebra SU_P (2), SU_q(1,1) and q-deformed boson operator. The energy spectra and E2 transition rates of ^110~114Cd iso topes are calculated. The calculated results agree with the experimental data rather well. Analyses on the calculated results show that the q-deformed U(5) limit is deviated from the symmetry in the original model and the degree of deviation is dependent on the deformation parameter.     

Approximate Analytical Solutions of the Dirac Equation with the Hyperbolic Potential in the Presence of the Spin Symmetry and Pseudo-spin Symmetry

By employing a new improved approximation scheme to deal with the centrifugal term and pseudo-centrifugal term, we solve approximately the Dirac equation with the hyperbolic potential for the arbitrary spin-orbit quantum number κ. Under the condition of the spin and pseudospin symmetry, the bound state energy eigenvalues and the associated two-component spinors of the Dirac particle are obtained approximately by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method.