Related papers: Discrete Liouville equation and Teichm\"uller theo…
The subject of our discussion is the theory of differential equations as set out in two classical Euler's textbooks "Institutiones Calculi Differentialis" and "Institutiones Calculi Integralis".
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
We review here some conventional as well as less conventional aspects of the time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its connections with Quantum Mechanics. Less conventional aspects involve the HJ theory on…
Taking quantum formalism as a point of reference and connection, we explore the various possibilities that arise in the construction of physical theories. Analyzing the distinct physical phenomena that each of them may describe, we…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
We give an algorithm for computing the Teichm\"uller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichm\"uller polynomial.
Discrete models of the Dirac-K\"{a}hler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral…
We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differential equation. The latter works directly on the…
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
Flat-space conformal invariance and curved-space Weyl invariance are simply related in dimensions greater than two. In two dimensions the Liouville theory presents an exceptional situation, which we here examine.
Motivated by recent works on the connection between 2D quantum gravity and timelike Liouville theory, we revisit the latter and clarify some aspects of the computation of its partition function: We present a detailed computation of the…
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first…
A formalism for describing charged particles interaction in both a finite volume and a uniform magnetic field is presented. In the case of short-range interaction between charged particles, we show that the factorization between short-range…
We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on $SL(2, \Real)$. The classical reduced system consists of a pair of Liouville…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
The origin of the rather mysterious duality symmetry found in quantum Liouville theory is investigated by considering the Liouville theory as the reduction of a WZW-like theory in which the form of the potential for the Cartan field is not…
The problem of constructing semi-discrete integrable analogues of the Liouville type integrable PDE is discussed. We call the semi-discrete equation a discretization of the Liouville type PDE if these two equations have a common integral.…