Related papers: Differential equations and integrable models: the …
Typically, the exact ground state energy of integrable models at finite volume can be computed using two main methods: the thermodynamic Bethe ansatz approach and the lattice discretization technique. For quantum sigma models (with…
By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space…
Covariant first and second quantization of the free d=4 massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of maslessness…
By generalizing the Feynman proof of the Lorentz force law, recently reported by Dyson, we derive equations of motion for particles possessing internal degrees of freedom $I^a$ which do not, in general, generate a finite algebra. We obtain…
We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical…
Starting from many quark interactions, we construct a nonlinear sigma-omega model at finite temperature and density. The mesons are introduced as auxiliary fields. Effective quark-meson couplings are strongly related to effective meson…
We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell states of a free closed string moving in a flat background. The dynamic equation corresponding to the condition of conformal…
A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field…
We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schr\"odinger algebra, these equations…
We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gr\"obner bases to clarify crucial notions concerning compatibility…
In our previous publications we have introduced a differential calculus on the algebra $U(gl(m))$ based on a new form of the Leibniz rule which differs from that usually employed in Noncommutative Geometry. This differential calculus…
The model of nonperturbative vacuum in SU(2) Yang-Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to…
We show that the one-dimensional projection of Chern-Simons gauged Nonlinear Schrodinger model is equivalent to an Abelian gauge field theory of continuum Heisenberg spin chain. In such a theory, the matter field has geometrical meaning of…
We formulate Friedmann's equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the $\beta$-times $t_\beta:=\int^t a^{-2\beta}$, where $a$ is the scale…
We consider a space-time with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform non-perturbative…
The edge state theory of a class of symmetric double-layer quantum Hall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the…
Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a…
In this paper, we study the existence of ground state solutions for the nonlinear fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^su+V(x)u+\phi u=|u|^{p-1}u, & \hbox{in $\mathbb{R}^3$,}…
We investigate the massive Sine-Gordon model in the finite ultraviolet regime on the two-dimensional Minkowski spacetime $(\mathbb{R}^2,\eta)$ with an additive Gaussian white noise. In particular we construct the expectation value and the…
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…