Semi-classical spectrum of the continuous Heisenberg spin chain

We develop a path integral formalism that allows for semi-classical quantization of systems with spin degrees of freedom. We apply it to study the continuous Heisenberg spin chain, which has been known to possess interesting classical solutions. The calculated semi-classical spectrum turns out to be essentially exact. We also construct a new infinite series of conservation laws that are nonlocal generalizations of the spin.     

Mass scales and crossover phenomena in the homogeneous sine-Gordon models

The finite-size behaviours of the homogeneous sine-Gordon models are analysed in detail, using the thermodynamic Bethe ansatz. Crossovers are observed which allow scales associated with both stable and unstable quantum particles to be picked up. By introducing the concept of shielding, we show that these match precisely with the mass scales found classically, supporting the idea that the full set of unstable particle states persists even far from the semiclassical regime. General rules for the effective TBA systems governing individual crossovers are given, and we also comment on the Lagrangian treatment of the theories, novel issues which arise in the form-factor approach for theories with unstable particles, and the role of heterotic cosets in the staircase flows exhibited by the HSG models.     

Exact form factors in integrable quantum field theories: the sine-Gordon model

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of ‘maximal analyticity” and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the “off-shell” Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three-particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.     

Abelian gauge theories on homogeneous spaces

An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S ³ is calculated. A generalization of the Chern-Simons action is suggested and analyzed with the example of SU(3)/U(1) X U(1).     

Pressure spectrum in homogeneous turbulence

The pressure spectrum in homogeneous steady turbulence is studied using direct numerical simulation with resolution up to 1024(3) and the Reynolds number R(lambda) between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant K = 1.65+/-0.05 followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately P(k) = B(p)epsilon;(4/3)k(-7/3) with B(p) = 8.0+/-0.5, and followed by a bump of nearly k(-5/3) at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.     

Exact form factors in integrable quantum field theories: the sine-Gordon model (II)

A general model independent approach using the ‘off-shell Bethe Ansatz’ is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive Thirring model. Exact expressions of all matrix elements are obtained for several local operators. In particular soliton form factors of charge-less operators as for example all higher currents are investigated. It turns out that the various local operators correspond to specific scalar functions called p-functions. The identification of the local operators is performed. In particular the exact results are checked with Feynman graph expansion and full agreement is found. Furthermore all eigenvalues of the infinitely many conserved charges are calculated and the results agree with what is expected from the classical case. Within the frame work of integrable quantum field theories a general model independent ‘crossing’ formula is derived. Furthermore the ‘bound state intertwiners’ are introduced and the bound state form factors are investigated. The general results are again applied to the sine-Gordon model. The integrations are performed and in particular for the lowest breathers a simple formula for generalized form factors is obtained.     

Differential integral equation for the spectrum of isotropic homogeneous turbulence

The double and triple velocity correlations for isotropic homogeneous turbulence are constructed and used in v. Kármán-Howarth differential equation for isotropic correlations; it is reduced to a differential integral equation for the spectrum of turbulence; it contains only one dependent function (5.2). The equation of energy, which follows from the above equation, can be reduced toHeisenberg's type of equation for the spectrum of turbulence (5.6). Eddies of the same order of magnitudeinteract; they partly generate partly destroy votricity. Small eddies (large wave numbersk)act on large eddies by mainly destroying them.     

On the soliton spectrum of field theories with character interactions

It is shown that a soliton ansatz in field theories where the interaction is determined by the characters of compact Lie groups can be reduced to the sine-Gordon equation with higher harmonics. The mass spectrum of the basic solitons and the one-loop quantum corrections to it are found for characters of adjoint representations of compact Lie groups with nontrivial center.     

On the spectrum of Kaluza-Klein theories with non-compact internal spaces

We investigate the conditions under which Kaluza-Klein theories with non-compact internal spaces admit a discrete spectrum.     

Semi-classical limit of scattering length

For scattering by a finite range potential, it is shown that the scattering length is convergent to the capacity of the support of the finite range potential in the semi-classical limit. This result has been already proved by use of probabilistic methods. Here we give an alternative proof without using any probabilistic idea. The proof is purely analytical and very simple.     

Semi-classical calculations of hot nuclei

We present semi-classical calculations of hot nuclei performed within the framework of the procedure recently introduced by Bonche, Levit and Vautherin in Hartree-Fock calculations, in order to take consistently into account the effects of continuum states. We use zero and second order Thomas-Fermi approximations for describing the kinetic and spin-orbit energies. After having introduced the ingredients of the formalism and given the main features of our resolution scheme of the Thomas-Fermi equations, we perform a detailed comparison of our calculations with Hartree-Fock results in order to test the accuracy of our model. We discuss the zero-temperature limit case where T² developments can be worked out. We show that, at low temperatures (T ≲ 2 MeV) the subtraction procedure is not indispensable, as expected from Hartree-Fock calculations. We also recall recent results obtained by using our formalism in estimating the temperature dependence of the level density parameter. As in Hartree-Fock calculations we find the existence of a limiting temperature T_lim beyond which the nucleus is unstable because of the Coulomb interaction. By comparing our theoretical values of T_lim with recent experimental data, we show that, in spite of the approximations in our model, this limiting temperature could be related to the actual disappearance of fusion-like processes in medium energy heavy-ion collisions.     

Semi-classical approximation to the liquid-particle model

Equation for the gas component of the density matrix, as defined for the nuclear volume in the Liquid-Particle Model, is related to Landau's zero-sound equation for a distribution function. Boundary conditions which determine the physical solution are deduced which are set at a certain effective sharp surface and couple the volume density vibrations to dynamics of diffused surface layer of the density.     

Modular invariance and the spectrum of two dimensional conformal field theories

Modular invariance has recently emerged as a powerful tool in conformal field theory. In conjunction with the representation theory of infinite dimensional Lie algebras, the study of modular invariance gave the spectrum of several families of theories. These include the minimal conformal models (Cardy and others), WZW theories which describe string propagation on group manifolds (Gepner and Witten) and parafermionic field theories (Gepner and Qiu). The minimal conformal models models were shown to be a product of two SU(2) WZW theories (Gepner). These results represent a step towards a complete classification of conformal field theories, an important goal both for the study of critical phenomena and string theory.     

Master variables and spectrum equations in large-N theories

Based on the loop-space effective action approach to the large-N limit, we consider the issue of constrained minimization and the problem of small fluctuations. The master variables are introduced to allow for an unconstrained minimization; the second derivative of the effective loop-space action with respect to these variables leads to master equations for the spectrum of particle states. We show that even though these variables contain redundant degrees of freedom, the only additional eigenvalues are of zero energy. We also establish a simplification through use of a reduced ansatz.     

Volume dependence of the energy spectrum in massive quantum field theories

The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L. The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner. At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example).     

The energy-mometum spectrum of strongly coupled lattice gauge theories

We prove the existence of isolated one-particle states in the full energy-momentum spectrum of strongly coupled lattice pure gauge theories. A new lower bound for the upper mass gap, improving previous estimates, is also obtained.     

Semi-classical theory of nuclear reactions

Semi-classical theory has previously been derived with assumptions contrary to the usual experimental situation, in particular that the wave packets describing the projectile are small. We show that the same answers are obtained with large wave packets.