Exact Solutions to the Two-dimensional BF and Yang-Mills Theories in the Light-cone Gauge

It is shown that the BRS-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the $\widetilde{B}^2$ term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang-Mills theory is also obtained.Comment: 11 pages, LaTe

Generalized Gauge Theories and Weinberg-Salam Model with Dirac-K\"ahler Fermions

We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.Comment: 33 pages, LaTe

Low- and Medium-Dispersion Spectropolarimetry of Nova V475 Sct (Nova Scuti 2003): Discovery of an Asymmetric High-Velocity Wind in a Moderately Fast Nova

We present low-resolution ($R\sim 90$) and medium-resolution ($R\sim 2500$) spectropolarimetry of Nova V475 Sct with the HBS instrument, mounted on the 0.91-m telescope at the Okayama Astrophysical Observatory, and with FOCAS, mounted on the 8.2-m Subaru telescope. We estimated the interstellar polarization toward the nova from the steady continuum polarization components and H$\alpha$ line emission components. After subtracting the interstellar polarization component from the observations, we found that the H$\alpha$ emission seen on 2003 October 7 was clearly polarized. In the polarized flux spectrum, the H$\alpha$ emission had a distinct red wing extending to $\sim +4900$ km s$^{-1}$ and a shoulder around $+3500$ km s$^{-1}$, showing a constant position angle of linear polarization \theta_{\rm *}\simeq 155\arcdeg\pm 15\arcdeg. This suggests that the nova had an asymmetric outflow with a velocity of $v_{\rm wind}\simeq 3500$ km s$^{-1}$ or more, which is six times higher than the expansion velocity of the ionized shell at the same epoch. Such a high-velocity component has not previously been reported for a nova in the `moderately fast' speed class. Our observations suggest the occurrence of violent mass-loss activity in the nova binary system even during the common-envelope phase. The position angle of the polarization in the H$\alpha$ wing is in good agreement with that of the continuum polarization found on 2003 September 26 ($p_{\rm *}\simeq 0.4$--0.6 %), which disappeared within the following 2 d. The uniformity of the PA between the continuum polarization and the wing polarization on October 7 suggests that the axis of the circumstellar asymmetry remained nearly constant during the period of our observations.Comment: 27 pages, 7 figures, accepted for publication in A

Synaptic Ras GTPase activating protein regulates pattern formation in the trigeminal system of mice

The development of ordered connections or "maps" within the nervous system is a common feature of sensory systems and is crucial for their normal function. NMDA receptors are known to play a key role in the formation of these maps; however, the intracellular signaling pathways that mediate the effects of glutamate are poorly understood. Here, we demonstrate that SynGAP, a synaptic Ras GTPase activating protein, is essential for the anatomical development of whisker-related patterns in the developing somatosensory pathways in rodent forebrain. Mice lacking SynGAP show only partial segregation of barreloids in the thalamus, and thalamocortical axons segregate into rows but do not form whisker-related patches. In cortex, layer 4 cells do not aggregate to form barrels. In Syngap(+/-) animals, barreloids develop normally, and thalamocortical afferents segregate in layer 4, but cell segregation is retarded. SynGAP is not necessary for the development of whisker-related patterns in the brainstem. Immunoelectron microscopy for SynGAP from layer 4 revealed a postsynaptic localization with labeling in developing postsynaptic densities (PSDs). Biochemically, SynGAP associates with the PSD in a PSD-95-independent manner, and Psd-95(-/-) animals develop normal barrels. These data demonstrate an essential role for SynGAP signaling in the activity-dependent development of whisker-related maps selectively in forebrain structures indicating that the intracellular pathways by which NMDA receptor activation mediates map formation differ between brain regions and developmental stage

Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra

The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is accommodated as a coproduct operation of (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. Algebraic formulation of path integral is perturbatively defined and Ward-Takahashi identity can be derived on the lattice. The claimed inconsistency of the link approach leading to the ordering ambiguity for a product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This could be seen as a generalization of spin and statistics relation on the lattice. From the consistency of this braiding structure of fields a grading nature for the momentum operator is required.Comment: 45 page

Characterization studies of 1-(4-cyano-2-oxo-1,2-dihydro-1-pyridyl)-3-(4-cyano-1,2-dihydro-1-pyridyl)propane formed from the reaction of hydroxide Ion with 1,3-Bis-(4-cyano pyridinium)propane

The aqueous alkaline reaction of 1,3-bis(4-cyanopyridinium)propane dibromide, a reactant constituted of two pyridinium rings linked by a three-methylene bridge, generates a novel compound,1 -(4-cyano-2-oxo-1,2-dihydro-1-pyridyl)-3-(4-cyano-1,2-dihydro-1-pyridyl)propane. The reaction pathway is attributed to the proximity of the OH- ion inserted between two pyridinium moieties, which occurs only in bis(pyridinium) derivatives connected by short methylene spacers, where charge-conformational effects are important.A reação em meio aquoso alcalino do dibrometo de 1,3-bis(4-cianopiridinium)propano, um composto constituído por dois anéis piridínicos conectados por uma ponte metilênica de três carbonos, gerou um novo composto, o 1-(4-ciano-2-oxo-1,2-diidro-1-piridil)-3-(4-ciano-1,2-diidro-1-piridil)propano. O resultado da reação é atribuído à proximidade do íon OH-, encapsulado entre os dois anéis piridínicos, fato este observado apenas em derivados bis-piridínicos conectados por pontes metilênicas de curta extensão, onde imperam efeitos de carga aliados à conformação.CNPqFAPESPFundação Araucári

Matrix formulation of superspace on 1D lattice with two supercharges

Following the approach developed by some of the authors in recent papers and using a matrix representation for the superfields, we formulate an exact supersymmetric theory with two supercharges on a one dimensional lattice. In the superfield formalism supersymmetry transformations are uniquely defined and do not suffer of the ambiguities recently pointed out by some authors. The action can be written in a unique way and it is invariant under all supercharges. A modified Leibniz rule applies when supercharges act on a superfield product and the corresponding Ward identities take a modified form but hold exactly at least at the tree level, while their validity in presence of radiative corrections is still an open problem and is not considered here.Comment: 25 page

Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.Comment: 4 pages, 3 figure