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We show that Casimir-force calculations for a finite number of non-overlapping obstacles can be mapped onto quantum-mechanical billiard-type problems which are characterized by the scattering of a fictitious point particle off the very same obstacles. With the help of a modified Krein trace formula the genuine/finite part of the Casimir energy is determined as the energy-weighted integral over the log-determinant of the multi-scattering matrix of the analog billiard problem. The formalism is self-regulating and inherently shows that the Casimir energy is governed by the infrared end of the multi-scattering phase shifts or spectrum of the fluctuating field. The calculation is exact and in principle applicable for any separation(s) between the obstacles. In practice, it is more suited for large- to medium-range separations. We report especially about the Casimir energy of a fluctuating massless scalar field between two spheres or a sphere and a plate under Dirichlet and Neumann boundary conditions. But the formalism can easily be extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or non-overlapping potentials/non-ideal reflectors., Comment: 14 pages, 2 figures, plenary talk at QFEXT07, Leipzig, September 2007, some typos corrected

Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s- and p-wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter., Comment: 11 pages, 6 figures; some new references added

In recent years a two-scale expansion was established to study reactions of the type N N -> N N pi within chiral perturbation theory. Then the diagrams of some subclasses that are invariant under the choice of the pion field no longer appear at the same chiral order. In this letter we show that the proposed expansion still leads to well defined results. We also discuss the appropriate choice of the heavy baryon propagator., Comment: 16 pages, 4 figures, minor corrections

Isospin-breaking effects in nuclear matter are studied in the framework of a medium-modified Skyrme model. The proposed effective Lagrangian incorporates both the medium influence of the surrounding nuclear environment on the single nucleon properties and an explicit isospin-breaking effect in the mesonic sector. The approach predicts that the neutron-proton mass difference decreases in isospin-symmetric nuclear matter but by a very small amount only., Comment: 8 pages, 4 figures, revised version

The scattering determinant for the scattering of waves from several obstacles is considered in the case of elastic solids with voids. The multi-scattering determinant displays contributions from periodic ray-splitting orbits. A discussion of the weights of such orbits is presented., Comment: MMWP05 conference proceeding. 10 pages, 3 figures

We report on a new force that acts on cavities (literally empty regions of space) when they are immersed in a background of non-interacting fermionic matter fields. The interaction follows from the obstructions to the (quantum mechanical) motions of the fermions caused by the presence of bubbles or other (heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea in the inner crust of a neutron star or superfluid grains in a normal Fermi liquid. The effect resembles the traditional Casimir interaction between metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields are replaced by fermionic matter fields. We show that the fermionic Casimir problem for a system of spherical cavities can be solved exactly, since the calculation can be mapped onto a quantum mechanical billiard problem of a point-particle scattered off a finite number of non-overlapping spheres or disks. Finally we generalize the map method to other Casimir systems, especially to the case of a fluctuating scalar field between two spheres or a sphere and a plate under Dirichlet boundary conditions., Comment: 8 pages, 2 figures, submitted to the Proceedings of QFEXT'05, Barcelona, Sept. 5-9, 2005

We present a simple formalism for the evaluation of the Casimir energy for two spheres and a sphere and a plane, in case of a scalar fluctuating field, valid at any separations. We compare the exact results with various approximation schemes and establish when such schemes become useful. The formalism can be easily extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or non-overlapping potentials/non-ideal reflectors., Comment: published version; 13 pages, 2 figures; add. material (in Sec.VI) and corrections (esp. in App.B)

These are the proceedings of the workshop on ``Effective Field Theories in Nuclear, Particle and Atomic Physics'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from December 13 to 17, 2005. The workshop concentrated on Effective Field Theory in many contexts. A first part was concerned with Chiral Perturbation Theory in its various settings and explored strongly its use in relation with lattice QCD. The second part consisted of progress in effective field theories in systems with one, two or more nucleons as well as atomic physics. Included are a short contribution per talk., Comment: 56 pages, mini proceedings of the 337. WE-Heraeus-Seminar "Effective Field Theories in Nuclear Particle and Atomic Physics," Physikzentrum Bad Honnef, Bad Honnef, Germany, December 13 -- 17, 2004

We consider the spin-isospin-independent central part of the residual nucleon-nucleon potential in finite spherical nuclei taking into account the deformation effects of the nucleons within the surrounding nuclear environment. It is shown that inside the nucleus the short-range repulsive contribution of the potential is increased and the intermediate attraction is decreased. We identify the growth of the radial component of the spin-isospin independent short-range part of the in-medium nucleon-nucleon interaction as the responsible agent that prevents the radial collapse of the nucleus., Comment: 9 pages, 3 eps figures

We describe the Fermionic Casimir effect in the case of two spherical superfluid scatterers immersed in a normal Fermi system. It is shown that due to the focusing property of Andreev reflection this new Casimir-like energy is significantly enhanced when compared to the case of normal scatterers with specular reflection., Comment: 7 pages, 4 eps figures, latex (with epl.cls)

These are the proceedings of the fourth international workshop on "Chiral Dynamics: Theory and Experiment" which was held at the University of Bonn, September 8-13, 2003. The workshop concentrated on the various experimental andtheoretical aspects of chiral dynamics, including for the first time in this series detailed discussions of lattice gauge theory. It consisted of an introductory lecture, plenary talks, working group talks and working group summaries. Included is a short contribution per talk., Comment: 162 pp, 10 figs, LaTeX2e, Mini-Proceedings of the Fourth International Workshop on Chiral Dynamics: Theory and Experiment (CD2003), Bonn, Germany, September 8-13, 2003

We present a brief account of two phenomena taking place in a neutron star crust: the Fermionic Casimir effect and the major density depletion of the cores of the superfluid neutron vortices., Comment: 6 pages, invited talk presented by AB at Tours 2003 Symposium on Nuclear Physics, August 26-29,Tours, France

We investigate the possible modifications of the nucleons' electromagnetic form factors in the framework of a modified Skyrme model allowing for nucleon deformation and using realistic nuclear mass distributions. We show that such effects are small in light nuclei., Comment: 5 pp, 2 figures

These are the proceedings of the workshop on ``Effective Field Theories of QCD'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from November 26 to 30, 2001. The workshop concentrated on Chiral Perturbation Theory in its various settings, its relations with lattice QCD and dispersion theory and the use of effective field theories in systems with one, two or more nucleons as well as at high baryon densities. Included are a short contribution per talk and a listing of some review papers on the subject., Comment: 58 pp, LaTeX2e, 2 figs, miniproceedings of the meeting on ``Effective Field Theories of QCD'', Bad Honnef, Germany, Nov.26-30, 2001

An explicit expression of the generating functional of two-flavor low-energy QCD with external sources in the presence of non-vanishing nucleon densities has been derived recently [1]. Within this approach we derive power counting rules for the calculation of in-medium pion properties. We develop the so-called standard rules for residual nucleon energies of the order of the pion mass and a modified scheme (non-standard counting) for vanishing residual nucleon energies. We also establish the different scales for the range of applicability of this perturbative expansion, which are \sqrt{6}\pi f_\pi\simeq 0.7 GeV for the standard and 6\pi^2 f_\pi^2/2m_N\simeq 0.27 GeV for non-standard counting, respectively. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions. In particular, we find a mass shift for negatively charged pions in heavy nuclei that agrees with recent determinations from deeply bound pionic Pb-207. We have also established the absence of in-medium renormalization in the \pi^0 \to \gamma\gamma decay amplitude up to the same order. The study of \pi\pi scattering requires the use of the non-standard counting and the calculation is done at leading order. Even at that order we establish new contributions not considered so far. We also point towards further possible improvements of this scheme and touch upon its relation to more conventional many-body approaches., Comment: 40 pages, 12 figures, version to appear in Ann. Phys

The deformation of a nucleon embedded in various finite nuclei is considered by taking into account the distortion of the chiral profile functions under the action of an external field representing the nuclear density. The baryon charge distribution of the nucleon inside light, medium-heavy and heavy nuclei is discussed. The mass of the nucleon decreases as it is placed deeper inside the nucleus and reaches its minimum at the center of the nucleus. We discuss the quantization of non-spherical solitons and its consequences for the mass splitting of the delta states. We show that bound nucleons acquire an intrinsic quadrupole moment due to the deformation effects. These effects are maximal for densities of nuclei about \rho(R)\sim 0.3...0.35 \rho(0). We also point out that scale changes of the electromagnetic radii can not simply be described by an overall swelling factor., Comment: 29 pp, REVTeX, 8 figures, more detailed discussion on quantization and intrinsic quadrupole moments, references added

The exact elastodynamic scattering theory is constructed to describe the spectral properties of two- and more-cylindrical cavity systems, and compared to an elastodynamic generalization of the semi-classical Gutzwiller unstable periodic orbits formulas. In contrast to quantum mechanics, complex periodic orbits associated with the surface Rayleigh waves dominate the low-frequency spectrum, and already the two-cavity system displays chaotic features., Comment: 7 pages, 5 eps figures, latex (with epl.cls)

We investigate the relevance of the instanton-induced determinantal 't Hooft interaction to the eta-nucleon coupling within the framework of a three-flavor linear sigma model in the OZI-rule-respecting basis. Instantons, in combination with the spontaneous breaking of chiral symmetry, are shown to provide the major mechanism for the ideal mixing between pseudoscalar strange and non-strange quarkonia. As long as 't Hooft's interaction captures most of the basic features of the axial QCD gluon anomaly, we identify the anomaly as the main culprit for the appearance of octet flavor symmetry in the anomalous sectors of the pseudoscalar (and axial vector) mesons. Within this context, unitary spin is shown to be an accidental symmetry due to anomalous gluon dynamics rather than a fundamental symmetry in its own right. Though we find the eta-nucleon coupling constant to obey a Goldberger-Treiman like relation, the latter does not take its origin from a pole dominance of the induced pseudoscalar form factor of the octet axial current, but from a subtle flavor-mixing mechanism that is traced back to instanton dynamics. The model presented allows for possible generalizations to non-ideal mixing angles and different values of the meson decay constants in the strange and non-strange sectors, respectively. Finally, we discuss the issue as to what extent the eta meson may be considered as a Goldstone boson under the constraints of the anomaly-produced unitary spin., Comment: 28 pages, LaTeX, 4 figures.ps, uses elsart.cls and graphicx

In a kinematically complete experiment at the Mainz microtron MAMI, pion angular distributions of the $^3$He(e,e'$\pi^+)^3$H reaction have been measured in the excitation region of the $\Delta$ resonance to determine the longitudinal ($L$), transverse ($T$), and the $LT$ interference part of the differential cross section. The data are described only after introducing self-energy modifications of the pion and $\Delta$-isobar propagators. Using Chiral Perturbation Theory (ChPT) to extrapolate the pion self energy as inferred from the measurement on the mass shell, we deduce a reduction of the $\pi^+$ mass of $\Delta m_{\pi^+} = (-1.7^{+ 1.7}_{- 2.1})$ MeV/c$^2$ in the neutron-rich nuclear medium at a density of $\rho = (0.057^{+ 0.085}_{- 0.057})$ fm$^{-3}$. Our data are consistent with the $\Delta$ self energy determined from measurements of $\pi^0$ photoproduction from $^4$He and heavier nuclei., Comment: Elsart, 12 pages and 4 figures, Correspondent: Professor Dr. Dr. h.c. mult. Achim Richter, richter@ikp.tu-darmstadt.de, submitted to Phys. Rev. Lett

Using ensembles of two, three and four spheres immersed in a fermionic background we evaluate the (integrated) density of states and the Casimir energy. We thus infer that for sufficiently smooth objects, whose various geometric characteristic lengths are larger then the Fermi wave length one can use the simplest semiclassical approximation (the contribution due shortest periodic orbits only) to evaluate the Casimir energy. We also show that the Casimir energy for several objects can be represented fairly accurately as a sum of pairwise Casimir interactions between pairs of objects., Comment: 4 pages, 5 figures, version to appear in PRL

QCD superconductors in the color-flavor-locked (CFL) phase sustain excitations (``Cooper'' mesons) that can be described as pairs of particles or holes around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy the masses, decay constants and form factors of the scalar, pseudoscalar, vector and axial-vector excitations, which explicitly are of finite size, can be calculated exactly. Furthermore, the constraints of this microscopic calculation on the effective-lagrangian description and the computation of the generalized triangle anomaly are discussed., Comment: 8 pages, LaTeX, 3 figures.eps, uses sprocl.sty, invited talk for Bologna 2000

QCD superconductors in the color-flavor-locked (CFL) phase support light excitations (generalized pions) in the form of particle-particle or hole-hole excitations. We analyze the generalized process $\tilde\pi^0\to\tilde{\gamma}\tilde{\gamma}$ in the weak coupling limit and show that it is related to the recently suggested Wess-Zumino-Witten (WZW) term. In dense QCD, the radiative decay of the generalized pion is constrained by geometry and vanishes at large density., Comment: 7 pages, 1 figure

QCD superconductors in the color-flavor-locked (CFL) phase support excitations (generalized mesons) that can be described as pairs of particles or holes (rather than particle-hole) around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy the scalar and pseudoscalar excitations are massless and the vector and axial-vector excitations are massive and degenerate. The massless scalar excitations are combined with the longitudinal gluons leading to the Meissner effect in the CFL phase. The mass of the composite vector excitations is close to twice the gap in weak coupling, but goes asymptotically to zero with increasing coupling thereby realizing Georgi's vector limit in cold and dense matter. We discuss the possible mixing of the composite scalar and vector excitations with the gluons, their possible coupling to the modified photons and their decay into light pseudoscalars in the CFL phase. The issue of hidden gauge-symmetry in the QCD superconductor is critically examined. The physical implications of our results on soft dilepton and neutrino emission in cold and dense matter are briefly discussed., Comment: 43 pages, 4 figures, further discussions and references added

QCD superconductors in the color-flavor-locked (CFL) phase sustain light Goldstone modes (that will be referred to as generalized pions) that can be described as pairs of particle and/or hole excitations around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy, their form factor, mass and decay constant can be evaluated exactly. These modes are found to satisfy an axial-Ward-identity, constraining the mass of the Goldstone modes in the CFL phase., Comment: 13 pages, 4 figures, version to be published in PLB

We discuss the Overhauser effect (particle-hole pairing) versus the BCS effect (particle-particle or hole-hole pairing) in QCD at large quark density. In weak coupling and to leading logarithm accuracy, the pairing energies can be estimated exactly. For a small number of colors, the BCS effect overtakes the Overhauser effect, while for a large number of colors the opposite takes place, in agreement with a recent renormalization group argument. In strong coupling with large pairing energies, the Overhauser effect may be dominant for any number of colors, suggesting that QCD may crystallize into an insulator at a few times nuclear matter density, a situation reminiscent of dense Skyrmions. The Overhauser effect is dominant in QCD in 1+1 dimensions, although susceptible to quantum effects. It is sensitive to temperature in all dimensions., Comment: 20 pages, 1 figure

The scattering problems of a scalar point particle from a finite assembly of n>1 non-overlapping and disconnected hard disks, fixed in the two-dimensional plane, belong to the simplest realizations of classically hyperbolic scattering systems. Here, we investigate 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. Our quantum-mechanical calculation is well-defined at every step, as the on-shell T-matrix and the multiscattering kernel M-1 are shown to be trace-class. The multiscattering determinant can be organized in terms of the cumulant expansion which is the defining prescription for the determinant over an infinite, but trace-class matrix. The quantum cumulants are then expanded by traces which, in turn, split into quantum itineraries or cycles. These can be organized by a simple symbolic dynamics. The semiclassical reduction of the coherent multiscattering part takes place on the level of the quantum cycles. We show that the semiclassical analog of the m-th quantum cumulant is the m-th curvature term of the semiclassical zeta function. In this way quantum mechanics naturally imposes the curvature regularization structured by the topological (not the geometrical) length of the pertinent periodic orbits onto the semiclassical zeta function. However, since the cumulant limit m->infinity and the semiclassical limit hbar->0 do not commute in general, the semiclassical analog of the quantum multiscattering determinant is a curvature expanded, truncated semiclassical zeta function. We relate the order of this truncation to the topological entropy of the corresponding classical system., Comment: 131 pages (LaTeX), 47 figures (PostScript), uses elsart.sty, epsfig.sty, epsf.sty and epsf.tex; Habilitationsschrift (TU Darmstadt), see http://crunch.ikp.physik.tu-darmstadt.de/~wirzba/Habilitation.html

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

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

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

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., Comment: 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., Comment: 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

We investigate the scattering off three nonoverlapping disks equidistantly spaced along a line in the two-dimensional plane with the radii of the outer disks equal and the radius of the inner disk varied. This system is a two-dimensional scattering analog to the double-well-potential (bound state) problem in one dimension. In both systems the symmetry splittings between symmetric and antisymmetric states or resonances, respectively, have to be traced back to tunneling effects, as semiclassically the geometrical periodic orbits have no contact with the vertical symmetry axis. We construct the leading semiclassical ``creeping'' orbits that are responsible for the symmetry splitting of the resonances in this system. The collinear three-disk-system is not only one of the simplest but also one of the most effective systems for detecting creeping phenomena. While in symmetrically placed n-disk systems creeping corrections affect the subleading resonances, they here alone determine the symmetry splitting of the 3-disk resonances in the semiclassical calculation. It should therefore be considered as a paradigm for the study of creeping effects. PACS numbers: 03.65.Sq, 03.20.+i, 05.45.+b, Comment: replaced with published version (minor misprints corrected and references updated); 23 pages, LaTeX plus 8 Postscript figures, uses epsfig.sty, espf.sty, and epsf.tex

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., Comment: replaced with published version; 16 pages, LaTeX{revtex}, no 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

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 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)

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., Comment: 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

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

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., Comment: 24 pages, LaTeX, TAN-FNT-93-12 (it replaces old version which was truncated)

As an alternative approach to the infinite-array description of dense matter in the Skyrme model, we report about the properties of a single skyrmion on a compact 3-sphere of finite radius. The density of this matter can be increased by decreasing the hypersphere radius. As in the array calculations one encounters a transition to a distinct high density phase characterized by a delocalization in energy and baryon charge and by increased symmetries. We will argue that the high density phase has to be interpreted as chirally restored one. The arguments are based on the formation of complete chiral multiplets and the vanishing of the pionic massless Goldstone modes in the high-density fluctuation spectrum. We show that the restoration of chiral symmetry is common to any chirally invariant extension of the usual Skyrme model - whether via higher-order contact terms or via the introduction of stabilizing vector mesons which act over a finite range. (Talk at the workshop on ``Baryons as Skyrme Solitons'', Siegen, Germany, Sept. 27-30, 1992), Comment: 20 pages, LaTeX, TH Darmstadt: IKDA 92/37

We show that color can leak from a QCD bag if we allow for pseudoscalar isoscalar singlet ($\eta'$) coupling at the surface. To enforce total confinement of color an additional boundary term is suggested. New relations between the $\eta'$ mass and decay constant and the QCD gluon condensates are derived and compared with the empirical parameters., Comment: 7 pages, LaTeX, Nordita - 92/68 N