BFV quantization on hermitian symmetric spaces

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.     

A generalization of Weyl's theorem on projectively related affine connections

From a physical point of view, the geodesics in a four-dimensional Lorentzian spacetime are really significant only as point sets. In 1921 Weyl proved that two torsion-free covariant derivative operators D_M and on a manifold M have the same geodesics with possibly different parametrizations if and only if there is a 1-form α on M such that , where 1 is the identity (1,1) tensor on M. By a theorem of Ambrose, Palais and Singer [1], torsion-free covariant derivative operators are generated by affine sprays, and vice versa. More generally, any (not necessarily affine) spray induces a number of covariant derivatives in the tangent bundle τ of M, or in the pull-back bundle τ∗τ. We show that in the context of sprays, similarly to Weyl's relation, a correspondence between the Yano derivatives can be detected.     

The decomposition of methanol on tungsten

In a simple cone-model of volume excitation for nearly free electron metals the resulting momentum distribution of excited electrons is shown to be anisotiopic in polycrystalline material with the bulk of excited electrons moving parallel to the electric field vector. Calculation of the yields Y_p for p-polarized light, and Y_s for s-polanzed light, from this momentum distribution gives large values of Y_p/Y_s and a characteristic photon energy dependence. Photoemission measurements at a gold-electrolyte interface are in qualitative agreement with the proposed model.     

Positivity of energy in Abelian principal bundles over spacetime

Five-dimensional classical unified field theories may be described in terms of the geometry of a five-dimensional Lorentz space V ₅.This space may be considered as a principal bundle over spacetime V ₄with metric g _ij and gauge group U(1). It has been shown that when V ₄is asymptotically flat, the total energy momentum vector of V ₅is nonspacelike, and that the gravitational mass of V ₄has a lower bound. These results obtain when V ₅is replaced by a Lorentzian space V _N ,a principal bundle over an asymptotically flat V ₄with an Abelian group G as its gauge group.     

Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting Q_BRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincaré symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.     

Fractional Fourier transform and geometric quantization

Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the “fractional Fourier transform” provides a simple example of this construction. As an application of this technique we show that for any linear Hamiltonian system, its quantum dynamics can be obtained exactly as the lift of the corresponding classical dynamics by means of the above transformation. Moreover, it can be deduced from the free quantum evolution. This way new, unknown symmetries of the Schrödinger equation can be constructed. It is also argued that the above construction defines in a natural way a connection in the bundle of quantum states, with the base space describing all their possible representations. The non-flatness of this connection would be responsible for the non-existence of a quantum representation of the complete algebra of classical observables.     

The Standard Model with one universal extra dimension

Effects of universal extra dimensions on Standard Model observables first arise at the one-loop level. The quantization of this class of theories is therefore essential in order to perform predictions. A comprehensive study of the SU _C(3) × SU _L(2) × U _Y(1) Standard Model defined in a space-time manifold with one universal extra dimension, compactified on the oribifold $S^1/Z_2$ , is presented. The fact that the four-dimensional Kaluza–Klein theory is subjected to two types of gauge transformations is stressed and its quantization under the basis of the BRST symmetry discussed. A SU _C(3) × SU _L(2) × U _Y(1)-covariant gauge-fixing procedure for the Kaluza–Klein excitations is introduced. The connection between gauge and mass eigenstate fields is established in an exact way. An exhaustive list of the explicit expressions for all physical couplings induced by the Yang–Mills, Currents, Higgs, and Yukawa sectors is presented. The one-loop renormalizability of the standard Green’s functions, which implies that the Standard Model observables do not depend on a cut-off scale, is stressed.     

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V^k$V^k$ to a decreasing family of k$k$ foliations _Fi$F_i$ on a manifold M$M$. We have shown that there exists a (1,1)$(1,1)$ tensor J$J$ of V^k$V^k$ such that J^k≠0$J^k\ne 0$, J^k+1=0$J^{k+1}=0$ and we defined by _LJ(V^k)$L_J\left(V^k\right)$ the Lie Algebra of vector fields X$X$ on V^k$V^k$ such that, for each vector field Y$Y$ on V^k$V^k$, [X,JY]=J[X,Y]$[X,JY]=J[X,Y]$.     

πη scattering and the resummation of vacuum fluctuation in three-flavor χPT

We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the s̄s pairs and the scenario with smaller value of the q̄q condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with πη scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p⁴) LECs, namely to the values of the fluctuation parameters L₄ and L₆. We discuss several issues in detail, namely the choice of “good” observables and properties of their bare expansions, the “safe” reparametrization in terms of physical observables, the implementation of exact perturbative unitarity and exact renormalization scale independence, the role of higher order remainders and estimates of their influence. We make a detailed comparison with standard chiral perturbation theory and use generalized χPT as well as resonance chiral theory to estimate the higher order remainders.     

Observables and quark confinement in the covariant canonical formalism of Yang-Mills theory

A concise criterion for observables in Yang-Mills theory is presented in the framework of covariant canonical field theory. As an example, the symmetric energy-momentum tensor θ_øν is proved to be an observable and its physically meaningful form is clarified. The validity of the “Maxwell-type” equation of motion is established in the physical subspace $\text{V}$_phys defined by the subsidiary condition $\text{Q}{}_{\mathrm{<mtext>B</mtext>}}\text{?}\text{phys}\text{〉 = 0}$ (Q_B: BRS charge). Its meaning and consequences are discussed in connection with the notion of observables: especially, all (quasi-) local observables in QCD are shown to be colour singlets and this fact paves the way to quark confinement.     

Symplectic Structures of Moduli Space¶of Higgs Bundles over a Curve and Hilbert Scheme¶of Points on the Canonical Bundle

The moduli space of triples of the form (E,θ,s) are considered, where (E,θ) is a Higgs bundle on a fixed Riemann surface X, and s is a nonzero holomorphic section of E. Such a moduli space admits a natural map to the moduli space of Higgs bundles simply by forgetting s. If (Y,L) is the spectral data for the Higgs bundle (E,θ), then s defines a section of the line bundle L over Y. The divisor of this section gives a point of a Hilbert scheme, parametrizing 0-dimensional subschemes of the total space of the canonical bundle K _X , since Y is a curve on K _X . The main result says that the pullback of the symplectic form on the moduli space of Higgs bundles to the moduli space of triples coincides with the pullback of the natural symplectic form on the Hilbert scheme using the map that sends any triple (E,θ,s) to the divisor of the corresponding section of the line bundle on the spectral curve. Received: 15 January 2000 / Accepted: 25 March 2001     

Nonlinear realizations of symmetry groups in terms of differential geometry

Nonlinear realizations of a symmetry group G, which become linear when restricted to a subgroup H are described in terms of fibre bundles. It is shown that so-called “covariant derivatives” occuring in nonlinear Lagrangians are equivalent to the covariant derivatives of the canonical connection in the principal bundle (G, G/H, H, δ). After the specification of a cross-section of the bundle, our formulae for the covariant derivatives coincide with those obtained by other authors in a group-theoretical way. In a special case where G is a chiral group and H is its diagonal subgroup, the canonical connection induces the Riemannian connection in the tangent bundle over G/H. For G = SU(2) × SU(2) and H = SU(2) this connection coincides with the Riemannian connection on the three-dimensional sphere introduced by K. Meetz.     

Limits on anomalous top couplings from Z pole physics

We obtain constraints on possible anomalous interactions of the top quark with the electroweak vector bosons arising from the precision measurements at the Z pole. In the framework of SU(2)_L ⊗ U(1)_Y chiral Lagrangians, we examine all effective CP-conserving operators of dimension five which induce fermionic currents involving the top quark. We constrain the magnitudes of these anomalous interactions by evaluating their one-loop contributions to the Z pole physics. Our analysis shows that the operators that contribute to the LEP observables get bounds close to the theoretical expectation for their anomalous couplings. We also show that those which break the SU(2)_C custodial symmetry are more strongly bounded.     

A see-saw model of sterile neutrino

If the smallness of the mass of the sterile neutrino is to be explained by the see-saw mechanism, the off-diagonal entries of the mass matrix needs to be protected by some symmetry not far above the electroweak scale. We implement see-saw mechanism in a gauge model based on SU(2)^q_L×SU(2)^l_L×U(1)^q_Y×U(1)^l_Y un-unified gauge group which breaks to SU(2)_L×U(1)_Y at the TeV region via a two-step symmetry breaking chain. The right handed diagonal block is tied to the highest scale up to which the un-unification symmetry holds. The sterile neutrino emerges from a quark-lepton mixed representation of the un-unified group.     

Numerical study of multi-hole SQUIDs using Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions

The I–V characteristics and the resultant total energies have been calculated full numerically for the parallel arranged multi-hole superconducting quantum interference devices (SQUIDs) consisting of Bi₂Sr₂CaCu₂O_8+δ high-T_c superconductors intrinsic Josephson junctions (BSCCO–IJJs). It has been found that (I) the effect of charge coupling between neighboring Josephson junctions is not so important, (II) the effect of noise is not so crucial except for the case of low β_L and no external magnetic field, and (III) a reliable external magnetic field dependence is obtained when the β_L is less than about 0.5, where the β_L is a dimensionless parameter defined by L_loopI_c/Φ₀ using a loop inductance L_loop of a SQUID, a critical current I_c of a junction, and a flux quantum Φ₀. We have pointed out that (IV) the steps which differ from Shapiro steps are found when an external ac modulation current is applied to the parallel arranged multi-hole SQUIDs, and (V) the I–V characteristics of a double hole BSCCO–IJJs–SQUID trapping a flux quantum can be controlled as a function of the external magnetic field.     

Quantization and the uniqueness of invariant structures

We determine and classify certain algebraic structures, defined on the space of all complex-valued polynomials in 2n real variables, which admitaffine contact transformations as automorphisms. These are the structures which have the minimum symmetry necessary to define the basic linear and angular momentum observables of classical and quantum mechanics. The results relate to the so-called Dirac problem of finding an appropriate mathematical characterization of the canonical quantization procedure.     

AlGaN/GaN场板结构高电子迁移率晶体管的场板尺寸优化分析

对不同场板尺寸的AlGaN/GaN 场板结构高电子迁移率晶体管进行了研究,建立简化模型分析场板长度对沟道电场分布的影响.结果表明,调整钝化层厚度和场板长度都可以调制沟道电场的分布形状,当场板长度较小时,随着长度的增大器件击穿电压随之增加,而当长度增大到一定程度后器件击穿电压不再增加.通过优化场板长度,器件击穿电压提高了64%,且实验结果与模拟结果相符. 关键词： AlGaN/GaN 击穿电压 场板长度     

Theoretical studies of the optical and EPR spectra for V in Y2O3 crystal

In this paper, we give an alternative suggestion that both the observed optical and electron paramagnetic resonance (EPR) spectra of Yttrium oxide (Y₂O₃):V³⁺ are attributed to V³⁺ ions at the S₆ site of Y₂O₃. This suggestion is different from the opinion in the previous paper that the optical and EPR spectra are attributed to V³⁺ ions at the C₂ and S₆ sites, respectively. From the suggestion, the optical band positions and spin-Hamiltonian parameters are calculated by diagonalizing the complete energy matrix for 3d² ions in trigonal symmetry. The results are in good agreement with the experimental values, suggesting that both the observed optical and EPR spectra in Y₂O₃:V³⁺ may be due to V³⁺ at S₆ site of Y₂O₃ crystal.