Related papers: A New Type of Conformal Dynamics
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
The macroscopic effects of the quantum conformal anomaly are evaluated in a simplified two-dimensional model of gravitational collapse. The effective action and stress tensor of the anomaly can be expressed in a local quadratic form by the…
We propose Lagrangian formulations of a three-particles translation invariant $N=4$ superconformal mechanics based on the standard and twisted $(1,4,3)$ supermultiplets. We show that in the appropriate set of coordinates, in which the…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
Tha quantum electrodynamics of particles constrained to move on a plane is not a fully dimensionally reduced theory because the gauge fields through which they interact live in higher dimensions. By constraining the gauge field to the…
The massive non-relativistic free particle in d-1 space dimensions has an action with a surprizing non-linearly realized SO(d,2) symmetry. This is the simplest example of a host of diverse one-time-physics systems with hidden SO(d,2)…
We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to…
The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…
We study teleparallel gravitational theories with are invariant under the conformal transformations. Wide family of the gravitational Lagrangians that are invariant under conformal transformations have investigated. Cosmological solutions…
We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying $ SU(1,1) $ symmetry, we find that the analytic solutions…
We provide a detailed construction of the quantum theory of the massless scalar field on 2-dimensional, globally-hyperbolic (in particular, Lorentzian) manifolds using the framework of perturbative algebraic quantum field theory. From this…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
In these lectures I review classical aspects of the self-dual Chern-Simons systems which describe charged scalar fields in $2+1$ dimensions coupled to a gauge field whose dynamics is provided by a pure Chern-Simons Lagrangian. These…
A universal model for D=4 spinning particle is constructed with the configuration space chosen as ${\bf R}^{3,1}\times S^2$, where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible…
We study a general scalar field Lagrangian coupled with matter and linear in $\Box\phi$ (also called KGB model). Within this class of models, we find the most general form of the Lagrangian that allows for cosmological scaling solutions,…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
We formulate a topological theory in six dimensions with gauge group SO(3,3) which reduces to gravity on a four dimensional defect if suitable boundary conditions are chosen. In such a framework we implement the reflection automorphism of…
We study solutions of the Klein-Gordon, Maxwell, and linearized Einstein equations in $\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primaries under the Lorentz group $SO(1,d+1)$. Such solutions, called conformal primary…
We study charged fluid spheres under the 4-dimensional Einstein-Maxwell space-time. The solutions thus obtained admitting conformal motion. We also investigate whether the solutions set provide electromagnetic mass models such that the…
Any conformally invariant energy associated with a curve possesses tension-free equilibrium states which are self-similar. When this energy is the three dimensional conformal arc-length, these states are the natural spatial generalizations…