Quantum and Classical Gauge Symmetries in a Modified Quantization Scheme

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the non-linear gauge $A_{\mu}^{2}=\lambda$ of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional {\em local} Faddeev-Popov formula {\em without} taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive non-gauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge invariant, has a more intrinsic meaning. It is suggested to extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.Comment: 14 pages. Substantially revised and enlarged including the change of the title. To appear in International Journal of Modern Physics

Induced top Yukawa coupling and suppressed Higgs mass parameters

In the scenarios with heavy top squarks, mass parameters of the Higgs field must be fine-tuned due to a large logarithmic correction to the soft scalar mass. We consider a new possibility that the top Yukawa coupling is small above TeV scale. The large top mass is induced from strong Yukawa interaction of the Higgs with another gauge sector, in which supersymmetry breaking parameters are given to be small. Then it is found that the logarithmic correction to the Higgs soft scalar mass is suppressed in spite of the strong coupling and the fine-tuning is ameliorated. We propose an explicit model coupled to a superconformal gauge theory which realizes the above situation.Comment: RevTeX4 style, 10 pages, 3 figure

Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

We investigate the relation between the diagonal ($\sigma_{xx}$) and off-diagonal ($\sigma_{xy}$) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value $-i \hbar /(2 \tau)$ with $\tau$ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width $\Gamma = \hbar /(2 \tau)$. Analytic formulas are obtained for both $\sigma_{xx}$ and $\sigma_{xy}$ within the framework of this simple approximation at low temperatures. By examining the leading terms in $\sigma_{xx}$ and $\sigma_{xy}$, we find a proportional relation between $\mathrm{d}\sigma_{xy}/\mathrm{d}B$ and $B \sigma_{xx}^2$. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.Comment: 21 pages, 8 figures, accepted for publication in J. Phys.: Condens. Matte

Spin-orbital gap of multiorbital antiferromagnet

In order to discuss the spin-gap formation in a multiorbital system, we analyze an e_g-orbital Hubbard model on a geometrically frustrated zigzag chain by using a density-matrix renormalization group method. Due to the appearance of a ferro-orbital arrangement, the system is regarded as a one-orbital system, while the degree of spin frustration is controlled by the spatial anisotropy of the orbital. In the region of strong spin frustration, we observe a finite energy gap between ground and first-excited states, which should be called a spin-orbital gap. The physical meaning is clarified by an effective Heisenberg spin model including correctly the effect of the orbital arrangement influenced by the spin excitation.Comment: 8 pages, 6 figures, extended versio

Universal Irreversibility of Normal Quantum Diffusion

Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of the systems, there exist a universal minimal quantum threshold above which the system completely loses the past memory, and the time-reversed dynamics as well as the time-reversal characteristics asymptotically trace universal curves independent of the details of the systems.Comment: 4 pages, 4 figure

Twists of newforms

AbstractLet Sk0(N, ψ) denote the subspace generated by newforms in the space of cuspforms of weight k and character ψ on Σ0(N). In this paper we study decompositions of Sk0(N, ψ) into direct sums of twists (by Dirichlet characters) of other spaces of newforms. Applied to individual newforms, these results immediately yield information on the behavior of newforms under character twists. Most of the results follow from applications of the Eichler Selberg formula for the traces of the Hecke operators. A version of this formula is given in the paper. A sample result is: Let p be a prime and let M be a positive integer prime to p. Let ω be a character mod pv with e = ordpf(ω) > v2 and let φ be a character mod M. Then Sk0(pvM, ωφ) = ⊕χ Sk0(peM, ωχ2φ)χ where the sum ⊕χ is over all primitive characters χ modulo pv − e and where Sk0(N, ψ)χ denotes the twist of Sk0(N,ψ) by χ

Max-plus analysis on some binary particle systems

We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.

Discovery of a lectin domain that regulates enzyme activity in mouse N-acetylglucosaminyltransferase-IVa (MGAT4A)

N-Glycosylation is a common post-translational modification, and the number of GlcNAc branches in N-glycans impacts glycoprotein functions. N-Acetylglucosaminyltransferase-IVa (GnT-IVa, also designated as MGAT4A) forms a β1-4 GlcNAc branch on the α1-3 mannose arm in N-glycans. Downregulation or loss of GnT-IVa causes diabetic phenotypes by dysregulating glucose transporter-2 in pancreatic β-cells. Despite the physiological importance of GnT-IVa, its structure and catalytic mechanism are poorly understood. Here, we identify the lectin domain in mouse GnT-IVa’s C-terminal region. The crystal structure of the lectin domain shows structural similarity to a bacterial GlcNAc-binding lectin. Comprehensive glycan binding assay using 157 glycans and solution NMR reveal that the GnT-IVa lectin domain selectively interacts with the product N-glycans having a β1-4 GlcNAc branch. Point mutation of the residue critical to sugar recognition impairs the enzymatic activity, suggesting that the lectin domain is a regulatory subunit for efficient catalytic reaction. Our findings provide insights into how branching structures of N-glycans are biosynthesized