Lie algebra cohomology and group structure of gauge theories

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other charge $Q^{\dagger}$.Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy

Collective modes of a helical liquid

We study low energy collective modes and transport properties of the "helical metal" on the surface of a topological insulator. At low energies, electrical transport and spin dynamics at the surface are exactly related by an operator identity equating the electric current to the in-plane components of the spin degrees of freedom. From this relation it follows that an undamped spin wave always accompanies the sound mode in the helical metal -- thus it is possible to `hear' the sound of spins. In the presence of long range Coulomb interactions, the surface plasmon mode is also coupled to the spin wave, giving rise to a hybridized "spin-plasmon" mode. We make quantitative predictions for the spin-plasmon in ${\rm Bi}_2{\rm Se}_3$, and discuss its detection in a spin-grating experiment.Comment: 4 Pages, 2 Figure

Charge and spin collective modes in a quasi-1D model of Sr2RuO4

Given that Sr2RuO4 is a two-component p-wave superconductor, there exists the possibility of well defined collective modes corresponding to fluctuations of the relative phase and spin-orientation of the two components of the order parameter. We demonstrate that at temperatures much below Tc, these modes have energies small compared to the pairing gap scale if the superconductivity arises primarily from the quasi 1D (dxz and dyz) bands, while it is known that their energies become comparable to the pairing gap scale if there is a substantial involvement of the quasi 2D (dxy) band. Therefore, the orbital origin of the superconductivity can be determined by measuring the energies of these collective modes.Comment: 11 pages (6 pages for main text), 2 figure

Majorana zero modes in a quantum Ising chain with longer-ranged interactions

A one-dimensional Ising model in a transverse field can be mapped onto a system of spinless fermions with p-wave superconductivity. In the weak-coupling BCS regime, it exhibits a zero energy Majorana mode at each end of the chain. Here, we consider a variation of the model, which represents a superconductor with longer ranged kinetic energy and pairing amplitudes, as is likely to occur in more realistic systems. It possesses a richer zero temperature phase diagram and has several quantum phase transitions. From an exact solution of the model these phases can be classified according to the number of Majorana zero modes of an open chain: 0, 1, or 2 at each end. The model posseses a multicritical point where phases with 0, 1, and 2 Majorana end modes meet. The number of Majorana modes at each end of the chain is identical to the topological winding number of the Anderson's pseudospin vector that describes the BCS Hamiltonian. The topological classification of the phases requires a unitary time-reversal symmetry to be present. When this symmetry is broken, only the number of Majorana end modes modulo 2 can be used to distinguish two phases. In one of the regimes, the wave functions of the two phase shifted Majorana zero modes decays exponentially in space but but in an oscillatory manner. The wavelength of oscillation is identical to the asymptotic connected spin-spin correlation of the XY-model in a transverse field to which our model is dual.Comment: 11 pages, 8 figures; brief clarifying comments added; few new references; this version is accepted in Phys. Rev.

Instanton solutions mediating tunneling between the degenerate vacua in curved space

We investigate the instanton solution between the degenerate vacua in curved space. We show that there exist $O(4)$-symmetric solutions not only in de Sitter but also in both flat and anti-de Sitter space. The geometry of the new type of solutions is finite and preserves the $Z_2$ symmetry. The nontrivial solution corresponding to the tunneling is possible only if gravity is taken into account. The numerical solutions as well as the analytic computations using the thin-wall approximation are presented. We expect that these solutions do not have any negative mode as in the instanton solution.Comment: Some typos are corrected and references are added with respect to the published version. 17pages, 11fi

CP1CP^{1} model with Hopf term and fractional spin statistics

We reconsider the $CP^{1}$ model with the Hopf term by using the Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of the Dirac quantization method. We also perform a semi-classical quantization of the topological charge Q sector by exploiting the collective coordinates to explicitly show the fractional spin statistics.Comment: 15 page

HI Fluctuations at Large Redshifts: II - the Signal Expected for GMRT

For the GMRT, we calculate the expected signal from redshifted HI emission at two frequency bands centered at 610 and 325 MHz. The study focuses on the visibility-visibility cross-correlations, proposed earlier as the optimal statistical estimator for detecting and analyzing this signal. These correlations directly probe the power spectrum of density fluctuations at the redshift where the radiation originated, and thereby provide a method for studying the large scale structures at large redshifts. We present detailed estimates of the correlations expected between the visibilities measured at different baselines and frequencies. Analytic fitting formulas representing the salient features of the expected signal are also provided. These will be useful in planning observations and deciding an optimal strategy for detecting this signal.Comment: 16 pages including 7 figures, published in JAp