Related papers: Massless Thirring model in canonical quantization …
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
Several important dynamical systems are in $\mathbb{R}^2$, defined by the pair of differential equations $(x',y')=(f(x,y),g(x,y))$. A question of fundamental importance is how such systems might behave quantum mechanically. In developing…
The zigzag model is a relativistic integrable $N$-body system describing the leading high-energy semiclassical dynamics on the worldsheet of long confining strings in massive adjoint two-dimensional QCD. We discuss quantization of this…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like…
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be…
We discuss the canonical quantization of systems formulated on discrete space-times. We start by analyzing the quantization of simple mechanical systems with discrete time. The quantization becomes challenging when the systems have…
We find a new vacuum of the Bethe ansatz solutions in the massless Thirring model. This vacuum breaks the chiral symmetry and has the lower energy than the well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of the…
We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
We unveil the dynamical equivalence of field theories with non-canonical kinetic terms and canonical theories with a volume element invariant under transverse diffeomorphisms. The proof of the equivalence also reveals a subtle connection…
The electromagnetic field is canonically quantized in the presence of a linear, dispersive and dissipative medium that is in uniform motion. Specifically we calculate the change in the normal modes of the coupled matter-field system and…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.
We consider a holographic quark model where the confinement is a consequence of the quark condensate. Surprisingly, the equation of motion of our holographic model can be mapped to the old spin-less bag model. Both models correctly…
It is shown that the Callan-Giddings-Harvey-Strominger theory on the cylinder can be consistently quantized (using Dirac's approach) without imposing any constraints on the sign of the gravitational coupling constant or the sign (or value)…
We introduce a statistical system on random networks of trivalent vertices for the purpose of studying the canonical tensor model, which is a rank-three tensor model in the canonical formalism. The partition function of the statistical…
A pedagogical introduction to solving classical and quantum many-body models in infinite spatial dimensions is given. The solution of the Hubbard model obtained in this limit is discussed in detail. It corresponds to a dynamical mean-field…