Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality

Multicomplex numbers of order n have an associated trigonometry (multisine functions with (n-1) parameters) leading to a natural extension of the sine-Gordon model. The parameters are constrained from the requirement of local current conservation. In two dimensions for n < 6 known integrable models (deformed Toda and non-linear sigma, pure affine Toda...) with dual counterparts are obtained in this way from the multicomplex space MC itself and from the natural embedding \MC_n \subset \MMC_m, n < m. For $n \ge 6$ a generic constraint on the space of parametersis obtained from current conservation at first order in the interaction Lagragien.Comment: 11 pages, no figure, LaTex with amsmath accepted by Phys. Lett.

Higgs mechanism in a light front formulation

We give a simple derivation of the Higgs mechanism in an abelian light front field theory. It is based on a finite volume quantization with antiperiodic scalar fields and a periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field that minimize the light front energy, is constructed. The corresponding effective Hamiltonian descibes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the space-like quantization, is derived without gauge fixing as well as in the unitary and the light cone gauge.Comment: 9 page

Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.Comment: 9 pages, 1 figure To be published in Physical Review

Critical properties of Φ1+14\Phi^4_{1+1}-theory in Light-Cone Quantization

The dynamics of the phase transition of the continuum $\Phi ^{4}_{1+1}$-theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter $$ in the form of dynamical zero mode operators (DZMO) which appear in a natural way via the Haag expansion of the field $\Phi (x)$ of the interacting theory. The inclusion of the DZM-sector changes significantly the value of the critical coupling, bringing it in agreement within 2% with the most recent Monte-Carlo and high temperature/strong coupling estimates. The critical slowing down of the DZMO governs the low momentum behavior of the dispersion relation through invariance of this DZMO under conformal transformations preserving the local light cone structure. The critical exponent $\eta$ characterising the scaling behaviour at $k^2 \to 0$ comes out in agreement with the known value 0.25 of the Ising universality class. $\eta$ is made of two contributions: one, analytic $(75$) and another (25%) which can be evaluated only numerically with an estimated error of 3%. The $\beta$-function is then found from the non-perturbative expression of the physical mass. It is non-analytic in the coupling constant with a critical exponent $\omega=2$. However, at D=2, $\omega$ is not parametrisation independent with respect to the space of coupling constants due to this strong non-analytic behaviour.Comment: Latex, 22 pages, 8 Postscript figures,Appendi

Scaling Laws and Transient Times in 3He Induced Nuclear Fission

Fission excitation functions of compound nuclei in a mass region where shell effects are expected to be very strong are shown to scale exactly according to the transition state prediction once these shell effects are accounted for. The fact that no deviations from the transition state method have been observed within the experimentally investigated excitation energy regime allows one to assign an upper limit for the transient time of 10 zs.Comment: 7 pages, TeX type, psfig, submitted to Phys. Rev. C, also available at http://csa5.lbl.gov/moretto/ps/he3_paper.p

Thermal fission rate around super-normal phase transition

Using Langer's $Im F$ method, we discuss the temperature dependence of nuclear fission width in the presence of dissipative environments. We introduce a low cut-off frequency to the spectral density of the environmental oscillators in order to mimic the pairing gap. It is shown that the decay width rapidly decreases at the critical temperature, where the phase transition from super to normal fluids takes place. Relation to the recently observed threshold for the dissipative fission is discussed.Comment: 12 pages, Latex, Submitted to Physical Review C for publication, 3 Postscript figures are available by request from [email protected]

Measurement of nuclide cross-sections of spallation residues in 1 A GeV 238U + proton collisions

The production of heavy nuclides from the spallation-evaporation reaction of 238U induced by 1 GeV protons was studied in inverse kinematics. The evaporation residues from tungsten to uranium were identified in-flight in mass and atomic number. Their production cross-sections and their momentum distributions were determined. The data are compared with empirical systematics. A comparison with previous results from the spallation of 208Pb and 197Au reveals the strong influence of fission in the spallation of 238U.Comment: 20 pages, 10 figures, background information at http://www-wnt.gsi.de/kschmidt

Infinite Nuclear Matter on the Light Front: Nucleon-Nucleon Correlations

A relativistic light front formulation of nuclear dynamics is developed and applied to treating infinite nuclear matter in a method which includes the correlations of pairs of nucleons: this is light front Brueckner theory. We start with a hadronic meson-baryon Lagrangian that is consistent with chiral symmetry. This is used to obtain a light front version of a one-boson-exchange nucleon-nucleon potential (OBEP). The accuracy of our description of the nucleon-nucleon (NN) data is good, and similar to that of other relativistic OBEP models. We derive, within the light front formalism, the Hartree-Fock and Brueckner Hartree-Fock equations. Applying our light front OBEP, the nuclear matter saturation properties are reasonably well reproduced. We obtain a value of the compressibility, 180 MeV, that is smaller than that of alternative relativistic approaches to nuclear matter in which the compressibility usually comes out too large. Because the derivation starts from a meson-baryon Lagrangian, we are able to show that replacing the meson degrees of freedom by a NN interaction is a consistent approximation, and the formalism allows one to calculate corrections to this approximation in a well-organized manner. The simplicity of the vacuum in our light front approach is an important feature in allowing the derivations to proceed. The mesonic Fock space components of the nuclear wave function are obtained also, and aspects of the meson and nucleon plus-momentum distribution functions are computed. We find that there are about 0.05 excess pions per nucleon.Comment: 39 pages, RevTex, two figure

The Nucleon Spectral Function at Finite Temperature and the Onset of Superfluidity in Nuclear Matter

Nucleon selfenergies and spectral functions are calculated at the saturation density of symmetric nuclear matter at finite temperatures. In particular, the behaviour of these quantities at temperatures above and close to the critical temperature for the superfluid phase transition in nuclear matter is discussed. It is shown how the singularity in the thermodynamic T-matrix at the critical temperature for superfluidity (Thouless criterion) reflects in the selfenergy and correspondingly in the spectral function. The real part of the on-shell selfenergy (optical potential) shows an anomalous behaviour for momenta near the Fermi momentum and temperatures close to the critical temperature related to the pairing singularity in the imaginary part. For comparison the selfenergy derived from the K-matrix of Brueckner theory is also calculated. It is found, that there is no pairing singularity in the imaginary part of the selfenergy in this case, which is due to the neglect of hole-hole scattering in the K-matrix. From the selfenergy the spectral function and the occupation numbers for finite temperatures are calculated.Comment: LaTex, 23 pages, 21 PostScript figures included (uuencoded), uses prc.sty, aps.sty, revtex.sty, psfig.sty (last included

Density Dependent Hadron Field Theory

A fully covariant approach to a density dependent hadron field theory is presented. The relation between in--medium NN interactions and field--theoretical meson--nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson--nucleon vertices on the baryon field operators. As a consequence, the Euler--Lagrange equations lead to baryon rearrangement self--energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy--momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean--field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac--Brueckner calculations with the Bonn NN-potentials are used. Results from Hartree calculations for energy spectra, binding energies and charge density distributions of $^{16}O$, $^{40,48}Ca$ and $^{208}Pb$ are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultanuous improvement of charge radii, charge densities and binding energies. The results indicate the appearance of a new "Coester line" in the nuclear matter equation of state.Comment: 48 LateX pages, 12 Figures, figures and full paper are available as postscript files by anonymous ftp at ftp://theorie.physik.uni-giessen.de/dd