Conformal invariance,current algebra and modular invariance

A large class of conformally invariant models in two dimensions is realised by constraining free fermion theories. The Fock spaces of the constrained theories are described, using the representation theory of affine Kac-Moody algebras. The results are extended to superconformally invariant theories. Projections of the models, producing consistent two-dimensional field theories, are discussed.     

Lorentz invariance of wave equations and galilean invariance of diffusion equations

The Lorentz invariance of a certain class of wave equations and on the other hand the galilean invariance of a certain class of diffusion equations is discussed.     

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.     

Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space–time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schrödinger invariance for θ=2.The hypothesis of local scale invariance implies that two-point functions of quasiprimary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time autoresponse function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber–Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics.     

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.     

Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

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.     

Conformal invariance and integration of first-order differential equations

This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.     

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.     

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.