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Two-point functions related to the pion weak decay constant f_\pi are calculated from the generating functional of chiral perturbation theory in the mean-field approximation and the heavy-baryon limit. The aim is to demonstrate that Lorentz invariance is violated in the presence of background matter. This fact manifests itself in the splitting of both f_\pi and the pion mass into uncorrelated time- and spacelike parts. We emphasize the different in-medium renormalizations of the correlation functions, show the inequivalence between the in-medium values of f_\pi deduced from Walecka-type models, on the one hand, and QCD sum rules, on the other hand, and elaborate on the importance for some nuclear physics observables., Comment: 14 pages, RevTex, no figures, to appear in Nucl.Phys. A

We investigate the scattering of a point particle from n non-overlapping, disconnected hard disks which are fixed in the two-dimensional plane and study the connection between the spectral properties of the quantum-mechanical scattering matrix and its semiclassical equivalent based on the semiclassical zeta function of Gutzwiller and Voros. We rewrite the determinant of the scattering matrix in such a way that it separates into the product of n determinants of 1-disk scattering matrices - representing the incoherent part of the scattering from the n disk system - and the ratio of two mutually complex conjugate determinants of the genuine multi-scattering kernel, M, which is of Korringa-Kohn-Rostoker-type and represents the coherent multi-disk aspect of the n-disk scattering. Our result is well-defined at every step of the calculation, as the on-shell T-matrix and the kernel M-1 are shown to be trace-class. We stress that the cumulant expansion (which defines the determinant over an infinite, but trace class matrix) imposes the curvature regularization scheme to the Gutzwiller-Voros zeta function and thus leads to a new, well-defined and direct derivation of the semiclassical spectral function. We show that unitarity is preserved even at the semiclassical level., Comment: 23 pages, latex with IOP journal preprint style, no figures; final version - considerably shortened

Most discussions of chaotic scattering systems are devoted to two-dimensional systems. It is of considerable interest to extend these studies to the, in general, more realistic case of three dimensions. In this context, it is conceptually important to investigate the quality of semiclassical methods as a function of the dimensionality. As a model system, we choose various three dimensional generalizations of the famous three disk problem which played a central role in the study of chaotic scattering in two dimensions. We present a quantum-mechanical treatment of the hyperbolic scattering of a point particle off a finite number of non-overlapping and non-touching hard spheres in three dimensions. We derive expressions for the scattering matrix S and its determinant. The determinant of S decomposes into two parts, the first one contains the product of the determinants of the individual one-sphere S-matrices and the second one is given by a ratio involving the determinants of a characteristic KKR-type matrix and its conjugate. We justify our approach by showing that all formal manipulations in these derivations are correct and that all the determinants involved which are of infinite dimension exist. Moreover, for all complex wave numbers, we conjecture a direct link between the quantum-mechanical and semiclassical descriptions: The semiclassical limit of the cumulant expansion of the KKR-type matrix is given by the Gutzwiller-Voros zeta function plus diffractional corrections in the curvature expansion. This connection is direct since it is not based on any kind of subtraction scheme involving bounded reference systems. We present numerically computed resonances and compare them with the corresponding data for the similar two-dimensional N-disk systems and with semiclassical calculations., Comment: 35 pages, LaTeX plus 8 Postscript figures, uses epsf.sty, epsfig.sty and epsf.tex

In this provocative book, Norman Wirzba argues that the doctrine of creation-as presented in the Bible and as developed through the centuries-actually holds the key to a true understanding of our place in the environment and our responsibility toward it. Wirzba contends that an adequate response to environmental destruction depends on a new formulation of ourselves as part of a larger whole, rather than as radically free individuals. Drawing on the work of biblical scholars, ecologists, agrarians, philosophers, theologians, and cultural critics, Wirzba develops a comprehensive worldview that grows out of the idea that the world is God's creation.

We present measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped such as a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally derived for quantum systems such as eigenvalue statistics and periodic orbits and obtain, according to a model of Berry and Robnik [J. Phys. A 17, 2413 (1984)], a mixing parameter of about 25%. In numerical simulations of the classical motion in the cup, the degree of chaoticity has been estimated. This leads to an invariant chaotic Liouville measure of about 45%. The difference between this figure and the mixing parameter is due to the limited accuracy of the statistical analysis, caused by both the fairly small number of 286 resonances and the rather poor desymmetrization of the microwave cavity. Concerning the periodic orbits of the classical system, we present a comparison with the length spectrum of the resonator and introduce a bouncing ball formula for electromagnetic billiards. \textcopyright{} 1996 The American Physical Society.

A "quasiclassical" approximation to the quantum spectrum of the Schroedinger equation is obtained from the trace of a quasiclassical evolution operator for the "hydrodynamical" version of the theory, in which the dynamical evolution takes place in the extended phase space $[q(t),p(t),M(t)] = [q_i, \partial_i S, \partial_i \partial_j S ]$. The quasiclassical evolution operator is multiplicative along the classical flow, the corresponding quasiclassical zeta function is entire for nice hyperbolic flows, and its eigenvalue spectrum contains the spectrum of the semiclassical zeta function. The advantage of the quasiclassical zeta function is that it has a larger analyticity domain than the original semiclassical zeta function; the disadvantage is that it contains eigenvalues extraneous to the quantum problem. Numerical investigations indicate that the presence of these extraneous eigenvalues renders the original Gutzwiller-Voros semiclassical zeta function preferable in practice to the quasiclassical zeta function presented here. The cumulant expansion of the exact quantum mechanical scattering kernel and the cycle expansion of the corresponding semiclassical zeta function part ways at a threshold given by the topological entropy; beyond this threshold quantum mechanics cannot resolve fine details of the classical chaotic dynamics., 33 pages, LaTeX with lamuphys.sty, epsf.sty, epsfig.sty macros, available at http://www.nbi.dk/~predrag/

We present first measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped like a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally derived for quantum systems like eigenvalue statistics and periodic orbits and obtain according to a model of Berry and Robnik a mixing parameter of about 25%. In numerical simulations of the classical motion in the cup the degree of chaoticity has been estimated. This leads to an invariant chaotic Liouville measure of about 45%. The difference between this figure and the mixing parameter is due to the limited accuracy of the statistical analysis, caused by both, the fairly small number of 286 resonances and the rather poor desymmetrization of the microwave cavity. Concerning the periodic orbits of the classical system we present a comparison with the length spectrum of the resonator and introduce a new bouncing ball formula for electromagnetic billiards., 9 pages (RevTex) , 10 figures included, full resolution figures are available upon request from hofferbert@linac.ikp.physik.th-darmstadt.de, to be published in Phys. Rev. E

The generating functional of heavy baryon chiral perturbation theory at order O(Q^2) in the mean field approximation (with a pseudoscalar source coupling which is consistent with the PCAC-Ward identities on the current quark level) has been exploited to derive Migdal's in--medium pion propagator. It is shown that the prediction for the density dependence of the quark condensate obtained on the composite hadron level by embedding PCAC within the framework of Migdal's approach to finite Fermi systems is identical to that resulting from QCD., replaced with published version; 16 pages, LaTeX{revtex}, no figures

The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassicaly. The non-trivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory., Comment: Latex article + 3 ps figures

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit expansion. This situation is formally similar to edge diffraction except that the disk radii introduce a length scale in the problem such that for wave lengths smaller than the order of the disk radius we recover the usual semi-classical approximation; however, for wave lengths larger than the order of the disk radius there is a qualitatively different behaviour. We test the theory by successfully estimating the positions of scattering resonances in geometries consisting of three and four small disks., Comment: Final published version - some changes in the discussion and the labels on one figure are corrected

Two-point functions related to the pion weak decay constant $f_\pi$ are calculated from the generating functional of chiral perturbation theory in the mean field approximation and the heavy-baryon limit. The aim is to demonstrate that Lorentz invariance is violated in the presence of background matter. This fact manifests itself in the splitting of both $f_\pi$ and the pion mass into uncorrelated time- and space-like parts. We emphasize the different in-medium renormalizations of the correlation functions, show the inequivalence between the in-medium values of $f_\pi$ deduced from Walecka-type models, on the one hand, and QCD sum rules, on the other hand, and elaborate on the importance for some nuclear physics observables., Comment: Talk given at Int. Symp. Non-Nucleonic Degrees of Freedom Detected in Nucleus, Sept. 2-5, 1996 (Osaka, Japan); 5 pages latex

We argue that the effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e.g. the PCAC choice. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other in-medium identities are studied in addition. Finally, several constraints on effective lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogenous nuclear matter are discussed. (Talk presented at the workshop ``Hirschegg '95: Hadrons in Nuclear Matter'', Hirschegg, Kleinwalsertal, Austria, January 16-21, 1995), Comment: 14 pages, LaTeX, some typographical errors corrected

Chiral effective lagrangians may differ in their prediction of meson-nucleon scattering amplitudes off-meson-mass-shell, but must yield identical S-matrix elements. We argue that the effective meson mass in nuclear matter obtained from chiral effective lagrangians is also unique. Off-mass-shell amplitudes obtained using the PCAC choice of pion field must therefore not be viewed as fundamental constraints on the dynamics, the determination of the effective meson mass in nuclear matter or the possible existence of meson condensates in the ground state of nuclear matter. This hypothesis is borne out by a calculation of the effective mass in two commonly employed formulations of chiral perturbation theory which yield different meson-nucleon scattering amplitudes off-meson-mass-shell., Comment: 23 pages, LaTeX, 2 Postscript figures (fig1.ps, fig2.ps)

We report about the calculation of the branching ratios of the yet unmeasured eta' decays into four pions, based on a combination of chiral perturbation theory and vector-meson dominance [1]. The decays eta' -> 2(pi^+pi^-) and eta' -> pi^+pi^-2pi^0 are P-wave dominated and can largely be thought to proceed via two rho resonances. Branching fractions of (1.0 +- 0.3) x 10^-4 and (2.4 +- 0.7) x 10^-4, respectively, are calculated which are not much lower than the current experimental upper limits. The decays eta' -> 4pi^0 and eta -> 4pi^0, in contrast, are D-wave driven [2] as long as conservation of CP symmetry is assumed, and are significantly further suppressed. Any experimental evidence for the decay eta -> 4pi^0 could almost certainly be interpreted as a signal of CP violation. The CP-violating amplitudes for eta', eta -> 4pi^0, induced by the QCD theta-term, are given as well.

The Gutzwiller trace formula is extended to include diffraction effects. The new trace formula involves periodic rays which have non-geometrical segments as a result of diffraction on the surfaces and edges of the scatter., 4 pages, LaTeX, 1 ps figure

An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and which correspond to creping waves. A new family of resonances in the two disk scattering system can be well described which is completely missing if only the traditional periodic orbits are used., Comment: 4 pages, latex/REVTEX, 2 PS figures

Dibaryons configurations are studied in the framework of the bound state soliton model. A generalized axially symmetric ansatz is used to determine the soliton background. We show that once the constraints imposed by the symmetries of the lowest energy torus configuration are satisfied all spurious states are removed from the dibaryon spectrum. In particular, we show that the lowest allowed state in the $S=-2$ channel carries the quantum numbers of the H particle. We find that, within our approximations, this particle is slightly bound in the model. We discuss, however, that vacuum effects neglected in the present calculation are very likely to unbind the H., 24 pages, LaTeX, TAN-FNT-93-12 (it replaces old version which was truncated)

We determine the $N_c$--dependence of the resonance contributions to the Adler--Weisberger sum rule for the inverse square $1/g_A^2$ of the axial charge coupling constant and show that in the large $N_c$ limit the contributions of the Roper-like excitations scale as $O(1/N_c)$. Consistency with the $1/N_c^2$ scaling of the $1/g_A^2$ term in the sum rule requires these contributions to cancel against each other., Comment: 10 pages, LaTeX, TH Darmstadt preprint IKDA 93/47, REVISED