Application of Dyson mapping to odd-mass nuclei

The Dyson mapping is applied to the analysis of low-lying collective states in odd-mass nuclei. The original fermion (quasiparticle) space is truncated to a collective subspace which consists of products of collective phonons and a single fermion (quasiparticle). This subspace is mapped on an ideal boson-fermion space by the Dyson mapping and a simple but non-hermitian hamiltonian is obtained. The eigenvalue equations for the hamiltonian are numerically solved for the cases of the unique-parity states in the odd-mass Rh isotopes. The results show that the Dyson mapping is quite useful for analyses of phonon-particle coupling in odd-mass nuclei.     

Non-abelian Cheshire cat bag models in 1+1 dimensions

Non-abelian Cheshire cat models are investigated in their lagrangian and hamiltonian formulations. The lagrangian bag boundary conditions are used to derive the form of non-abelian soliton operators, through which fermions are represented in bosonic language. These soliton operators are then used to construct the boundary interaction in the hamiltonian picture, wherein the bosonic sector is formulated by means of a current algebra involving anomalous commutators. The hamiltonian and the momentum operator are shown to commute, thus implying that the Cheshire cat criterion — the independence of the energy spectrum on the bag wall position — is fulfilled by the system.     

The bosonic string in non-conformal gauges

The lagrangian and hamiltonian formalism for a free bosonic relativistic string are considered for arbitrary non-orthonormal or non-orthonormal gauges. We show in detail how one can write an arbitrary metric tensor as a reparametrization of a conformally flat one. By means of this decomposition, the lagrangian and hamiltonian formalisms are explicitly solved. From the result of this classical analysis we are then able to conclude that the quantization yields the same physical results as in the standard orthonormal gauge.We also comment on singularities in Liouville theories for strings.     

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green's function method. Taking the weakly bound nucleus ~(66)Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.     

Classical Electrodynamics of Point Charges

A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once removed without affecting the locality and the relativistic covariance of the theory, and with no need for mass renormalization. The procedure is first used to obtain a finite expression for the electromagnetic energy-momentum of the system. We show that the relativistic Lorentz-Dirac equation can be deduced from the conservation of this electromagnetic energy-momentum plus the usual mechanical term. Then we derive a finite lagrangian, which depends on the particle variables and on the actual electromagnetic potentials at a given time. From this lagrangian the equations of motion of both particles and fields can be derived via Hamilton's variational principle. The hamiltonian formulation of the theory can be obtained in a straightforward way. This leads to an interesting comparison between the resulting divergence-free expression of the hamiltonian functional and the standard renormalization rules for perturbative quantum electrodynamics.     

Defining Euler-Lagrange fields in terms of almost tangent structures

It is shown that a differentiable manifold with an almost tangent structure provides a suitably general setting for lagrangian dynamics, in analogy to the way that a symplectic manifold provides a suitably general setting for hamiltonian dynamics; and it is shown how a closed 1-form on a manifold with almost tangent structure determines a vector field, its Euler-Lagrange field, whose integral curves are solutions of the Euler-Lagrange equations for a suitable lagrangian function.     

Linearized structures of lagrangian,hamiltonian, and quasi-hamiltonian systems

Linearized structures are found for general lagrangian, hamiltonian, and quasi-hamiltonian systems, as well as for Lax and zero-curvature representations.     

On Anomalies in Classical Dynamical Systems

Abstract

The definition of “classical anomaly” is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure, close an algebra which is just the centrally extended version of the original symmetry algebra. The consistency conditions for this to occur are derived. Explicit examples are given based on simple two-dimensional models. Applications of the above scheme and lines of further investigations are suggested.     

Ideal incompressible hydrodynamics in terms of the vortex momentum density

Equations satisfied by the vortex momentum density are derived and are transformed into hamiltonian form. New lagrangian invariants are found with the help of these equations. The case in which the flow is representable by the known Clebsch potentials is analysed.     

Hamiltonian formulation of anomaly free chiral bosons

Starting out with an anomaly free lagrangian formulation for chiral scalars, which includes a Wess-Zumino term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Then we use the (quantum) Siegel invariance to choose a particular solution, which turns out to coincide with the one obtained by Floreanini and Jackiw.     

Non-invariance symmetries and constants of the motion

It is shown that conserved quantities for lagrangian systems can be associated with symmetry groups which do not leave the action integral invariant. An analogy with a recently described invariant for hamiltonian systems is pointed out.     

Classical superstring mechanics

We describe the classical mechanics of the superstring in both hamiltonian and lagrangian formulations, including massless external fields. The formulation is a modification of that of Green and Schwarz that allows supersymmetric Lorentz covariant quantization.     

Canonical quantization of the electromagnetic field with Dirac's monopoles

From a lagrangian theory of charge-monopole electrodynamics which uses strings but is free from Dirac's veto, a hamiltonian theory is derived which describes the interaction between electric and magnetic point particles and photons.     

Anharmonicities of γ-vibrations in 168Er

The multiphonon method, which is mainly an exact diagonalisation of the total hamiltonian in the collective space, is applied to the analysis of the γ-vibrations in ¹⁶⁸Er. The results are compared to those obtained by Dumitrescu and Hamamoto in a perturbation treatment and by Matsuo and Matsuyanagi in the self-consistent collective coordinate method. It is also explained why the quasiparticle phonon model of Soloviev strongly overestimates the energies of the two phonon states.     

Lorentz-covariant dissipative lagrangian systems

The concept of dissipative hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.     

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (I). Formulation

A normal-ordered linked-cluster boson expansion theory, previously worked out by one of the authors (T.K.) and Tamura, has been developed further by reformulating it in a “physical” quasiparticle subspace which contains no spurious particle-number excitation modes. The expansion coefficients of the collective hamiltonian for low-lying quadrupole motions are determined starting from a microscopic fermion hamiltonian including self-consistent higher-order (many-body) interactions derived in our previous work. The contributions from the non-collective states with all possible non-collective one-boson excitations having I^π = 0⁺− 4⁺, which can directly couple to the collective states with one or two phonons, are taken into account in a systematic and compact way.     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.     

Quasilinear Approximation and WKB

Quasilinear solutions of the radial Schrödinger equation for different potentials are compared with corresponding WKB solutions. For this study, the Schrödinger equation is first cast into a nonlinear Riccati form. While the WKB method generates an expansion in powers of , the quasi-linearization method (QLM) approaches the solution of the Riccati equation by approximating its nonlinear terms by a sequence of linear iterates. Although iterative, the QLM is not perturbative and does not rely on the existence of any kind of smallness parameters. If the initial QLM guess is properly chosen, the usual QLM solution, unlike the WKB, displays no unphysical turning-point singularities. The first QLM iteration is given by an analytic expression. This allows one to estimate analytically the role of different parameters, and the influence of their variation on the boundedness or unboundedness of a critically stable quantum system, with much more precision than provided by the WKB approximation, which often fails miserably for systems on the border of stability. It is therefore demonstrated that the QLM method is preferable over the usual WKB method.