From Skyrmions to NN phaseshifts

We study the $NN$ phaseshifts in a Hamiltonian obtained from quantization of the collective modes in the Skyrme model. We show that a combination of an adiabatic and diabatic approximation gives a good $NN$ force, with sufficient attraction to produce a bound deuteron. The description of the repulsive core appears to be the main cause for the remaining discrepancies between the Skyrme model force and phenomenology. Finally we discuss the possibility of finding non-strange dibaryon resonances in the $J^\pi=3^+$ channel

Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics

The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of $^{28}$Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other topics included are a nuclear Born-Oppenheimer approximation for an {\em ab initio} quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included.Comment: 203 pages, many figure

Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

Towards a phase diagram of the 2D Skyrme model

We discuss calculations of the phase diagram of the baby-Skyrme model, a two-dimensional version of the model that has been so successful in the description of baryons. Contact is made with the sine Gordon model in 1D, and relations with the Skyrme model used in the quantum-Hall effect are pointed out. It is shown that at finite temperature the phase diagram is dominated by a liquid, and not the crystal that plays a role for zero temperature

Exact renormalization group and many-fermion systems

The exact renormalization group methods is applied to many fermion systems with short-range attractive force. The strength of the attractive fermion-fermion interaction is determined from the vacuum scattering length. A set of approximate flow equations is derived including fermionic and bosonic fluctuations. The numerical solutions show a phase transition to a gapped phase. The inclusion of bosonic fluctuations is found to be significant only in the small-gap regime.Comment: Talk, given by B. Krippa on the International Workshop "Meson2004", Cracow, Poland, 3 page

Large Amplitude Collective Motion in Nuclei and Metallic Clusters: Applicability of adiabatic theory for a pairing model

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system

Quantum theory of large amplitude collective motion and the Born-Oppenheimer method

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for the results found previously in leading approximation, but also facilitates an extension of the theory to include an approximate description of the fast variables and their interaction with the slow ones. Among other corrections, one encounters the Berry vector and scalar potential. The formalism is illustrated with the aid of some simple examples, where the potentials in question are actually evaluated and where the accuracy of the Born Oppenheimer approximation is tested. Variational formulations of both Hamiltonian and Lagrangian type are described for the equations of motion for the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf styl

Towards a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory

We develop a consistent approach to Hamiltonian lattice gauge theory, using the maximal-tree gauge. The various constraints are discussed and implemented. An independent and complete set of variables for the colourless sector is determined. A general scheme to construct the eigenstates of the electric energy operator using a symbolic method is described. It is shown how the one-plaquette problem can be mapped onto a N-fermion problem. Explicit solutions for U(1), SU(2), SU(3), SU(4), and SU(5) lattice gauge theory are shown