Algebraic solutions of integrodifferential CRPA equations

We formulate a version of the collisional Random-Phase-Approximation obtained from the linearization of a general kinetic equation. The resulting equations are formally solved in three different situations depending on the way the previous history is considered. An application of the formalism here developed to a two level model is made.     

Gauge invariance and the generalized Bondi-Metzner algebra

We examine the algebraic meaning of the Electromagnetic gauge invariance and show that it leads to the new concepts of gauged operators, gauged representations and hence to infinite dimensional extensions of Lie algebras. In particular we prove that the generalized Bondi-Metzner algebra can be interpreted as a gauged Lorentz algebra related to the Electromagnetic gauge.     

The inhomogeneous invariance quantum supergroup of supersymmetry algebra

We consider an inhomogeneous quantum supergroup which leaves invariant a supersymmetric particle algebra. The quantum sub-supergroups of this inhomogeneous quantum supergroup are investigated.     

Two-dimensional integrodifferential equations for unequal mass particle systems

The two-variable Integrodifferential Equation Approach (IDEA) valid for A nucleons is generalized to describe quantum mechanical systems consisting of A, unequal mass, particles. The method is based on an expansion of the wave function in Faddeev amplitudes for the various particle pairs and a subsequent expansion of them in terms of Potential Harmonics. Projecting the resulting Faddeev-type equations on a specific two-body space and spin-isospin channel one obtains coupled, two-variable, integrodifferential equations describing the system. These equations can be readily applied, for example, to hypernuclear systems such as the double hypernucleus ΛΛα which can be handled either as a three- or as a six-body problem. We demonstrate our approach by applying it to various single and double hypernuclei and compare the results to those obtained by other methods.     

General criterion of invariance forintegro-differential equations

General criterion of invariance of integro-differential equations under Lie symmetry groupof point transformations is derived. It is a generalization of the previous form of the criterion to the case of a moving range of integration. This is the situation when a region of integration depends on external, with respect to integration, variables which leads to its explicit dependence on a group parameter.     

Local duality invariance of Maxwell equations

It is shown that the gauge-particle associated with local-duality transformation of Maxwell electro-magnetic equations is a massless axial vector boson which mediates universal long-range interaction between spins. Possible existence of a pure gauge field of this type in an inhomogeneous magneto-electric material is examined.     

Lie symmetry algebra of one-dimensional nonconservative dynamical systems

Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1--1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.     

Galilean and dynamical invariance of entanglement in particle scattering

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.     

Kane model,dynamical algebra and coherent states

Dynamical invariance algebra is developed for the Kane model. On the basis of the Heisenberg-Weyl algebra of invariants explicit expressions for interband coherent states and Green functions are derived.     

Entanglement via permutation symmetry and reflection invariance of angular momentum algebra

We propose an alternative method for computing total angular momentum using su(2)-invariance     

Clifford algebra structure and Einstein's equations

We point out that a Clifford algebra representation for the Riemannian curvature leads to an equation for gravity similar to the Yang-Mills equation, in a gauge model for gravity with the Lorentz group. Einstein's equation of general relativity emerges as a natural solution in this approach.     

The dynamical equations of black-body radiation

The dynamical equations for black-body radiation are derived from the vanishing of the stress-energy tensor and shown to imply a theorem which generalizes that of Tolman and Ehrenfest[Phys. Rev. 36,1791 (1930)]. A method for finding the general solution of these equations is given.Dedicated to Nathan Rosen with the affection of the author.     

Conformal invariance of Maxwell's equations with magnetic charges

It is shown that Maxwell's equations when there exist isolated magnetic charges are invariant under conformal transformations.     

On dynamical symmetry algebra for aq-extension of the harmonic oscillator

Dynamical symmetry algebra for aq-analogue of the linear harmonic oscillator in quantum mechanics is explicitly constructed in terms ofq-difference raising and lowering operators, which factorize governing Hamiltonian for this model.     

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

A three-parameter deformation of the Weyl-Heisenberg algebra: differential calculus and invariance

We define a three-parameter deformation of the Weyl-Heisenberg algebra that generalizes the q-oscillator algebra. By a purely algebraical procedure, we set up on this quantum space two differential calculi that are shown to be invariant on the same quantum group, extended to a ten-generator Hopf-star-algebra. We prove that when the values of the parameters are related, the two differential calculi reduce to one that is invariant under two quantum groups.     

Discrete dynamical equations in Minkowski space

Discrete difference equations in Minkowski space are obtained and the discrete Minkowski force is shown to be a four-vector. A transformation from a discrete dynamical equation in Minkowski space to a Lorentz-invariant difference equation in one-dimensional space is given.     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

Nonlinear transport equations and invariance principles for solids

The nonlinear hydrodynamic equations of motion for simple solids are derived. They are shown to be invariant under arbitrary homogeneous displacements, rotations, and deformations of the reference lattice. This leads to transport equations that are independent of a reference state. Galilean invariance is investigated too.