Related papers: Invariant Gibbs measures for the 2-d defocusing no…
We present an invariant regularisation scheme to compute two dimensional induced gauge theory actions, that is local in Polyakov's variables, but nonlocal in the original gauge potentials. Our method sheds light on the locality of this…
We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…
In the leading order of a modified 1/Nc expansion, we show that a class of gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined theories in the continuum limit. The renormalized Yukawa coupling y and the quartic…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
We are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean field wave functions by using the extension of the statistical Wick's theorem (Gaudin's theorem) in the appropriate limits.
A gauge invariant regularisation which can be used for non-perturbative treatment of Yang-Mills theories within the exact renormalization group approach is constructed. It consists of a spontaneously broken SU(N|N) super-gauge extension of…
We briefly review a recently proposed scheme for a gauge-invariant treatment of tadpole corrections in spontaneously broken gauge theories called Gauge-Invariant Vacuum expectation value Scheme (GIVS). The tadpole scheme matters in…
The non-commutative version of the euclidean $g^2\phi^4$ theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector…
I study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic noncovariant gauges where the Wilsonian infrared cutoff $\Lambda$ is inserted as a mass term for the propagating fields. In this way the Ward-Takahashi…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
The Whitham modulation equations for the defocusing nonlinear Schrodinger (NLS) equation in two, three and higher spatial dimensions are derived using a two-phase ansatz for the periodic traveling wave solutions and by period-averaging the…
Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg-Landau (TDGL) equation of a disturbance amplitude starting from a set of…
Second-order tensor modes induced by nonlinear gravity are a key component of the cosmological background of gravitational waves. A detection of this background would allow us to probe the primordial power spectrum at otherwise inaccessible…
The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered…
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a…
We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based Epstein-Glaser approach to…
A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based…
We study nonlinear internal gravity waves (IGWs) in the atmosphere. The reductive perturbation method is used to derive a system of two-dimensional nonlinear equations for the envelope of velocity stream function and the mean flow. In the…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…