Related papers: Schwarzian mechanics via nonlinear realizations
Grid-based discretizations of the time dependent Schr\"odinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice…
A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $\Gamma_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known…
We quantize the chiral Schwinger Model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first class constraints and the desired involutive Hamiltonian, which naturally generates all secondary…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field.…
We consider additive Schwarz methods for boundary value problems involving the $p$-Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for these methods, empirical evidence from numerical experiments…
The Schwarzian derivative has recently received renewed attention in connection with the study of the Sachdev-Ye-Kitaev model. In mathematics literature, various higher order generalizations of the Schwarzian derivative are known due to…
Because of all the known integrable models possess Schwarzian forms with M\"obious transformation invariance, it may be one of the best way to find new integrable models starting from some suitable M\"obious transformation invariant…
We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion…
The method of nonlinear realizations is applied to construct new dynamical realizations of the Lifshitz group in mechanics, hydrodynamics, and field theory.
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
The Schwarzian derivative provides a classical analytic measure of how far a holomorphic map of the disk is from being M\"obius, with Nehari's bounds giving sharp criteria for univalence. Independently, Thurston introduced a geometric…
The Lagrangian of self-dual gauge theory in various formulations are reviewed. From these results we see a simple rule and use it to present some new non-covariant Lagrangian based on the decomposition of spacetime into $D=D_1+D_2+D_3$. Our…
Within the framework of Lagrangian variables, we develop a method for deriving explicit solutions to the 2D Boussinesq equations using harmonic mapping theory. By reformulating the characterization of flow solutions described by harmonic…
We define a `non-relativistic conformal method', based on a Schr\"odinger algebra with critical exponent z = 2, as the non-relativistic version of the relativistic conformal method. An important ingredient of this method is the occurrence…
Lagrange introduced the notion of Schwarzian derivative and Thurston discovered its mysterious properties playing a role similar to that of curvature on Riemannian manifolds. Here we continue our studies on the development of the Schwarzian…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
In this paper we study the modular differential equation $y''+s\,E_4\, y=0$ where $E_4$ is the weight 4 Eisenstein series and $s=\pi^2r^2$ with $r=n/m$ being a rational number in reduced form such that $m\geq 7$. This study is carried out…
We study the Calder\'on problem for a logarithmic Schr\"odinger type operator of the form $L_{\Delta} +q$, where $L_{\Delta}$ denotes the logarithmic Laplacian, which arises as formal derivative $\frac{d}{ds} \big|_{s=0}(-\Delta)^s$ of the…
Two dimensional conformal field theories, can be described by their pseudo Goldstone bosons when the conformal symmetry is spontaneously and anomalously broken. We show that the Schwarzian action of these bosons leads to the Cardy formula…