arXiv subjects

Andreas Wirzba

Publications and source records attributed to Andreas Wirzba.

36 records · Page 2Linked to original sources

arXiv2001

Instantons As Unitary Spin Maker

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.

nucl-th↗

arXiv2001

Casimir Interaction among Objects Immersed in a Fermionic Environment

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.

nucl-th↗

arXiv2000

Cooper-Mesons in the Color-Flavor-Locked Superconducting Phase of Dense QCD

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.

nucl-th↗

arXiv2000

Pi0 -> Gamma Gamma in Dense QCD

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 $\tildeπ^0\to\tildeγ\tildeγ$ 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.

hep-ph↗

arXiv2000

Generalized Mesons in Dense QCD

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.

hep-ph↗

arXiv1999

Generalized Pions in Dense QCD

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.

hep-ph↗

arXiv1999

Dense QCD : Overhauser or BCS Pairing ?

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.

hep-ph↗

arXiv1998

A direct link between the quantum-mechanical and semiclassical determination of scattering resonances

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.

chao-dyn↗

arXiv1997

Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems

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.

chao-dyn↗

arXiv1997

Quantization of Hyperbolic N-Sphere Scattering Systems in Three Dimensions

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.

chao-dyn↗

arXiv1997

In-Medium Chiral Perturbation Theory and Pion Weak Decay in the Presence of Background Matter

Two-point functions related to the pion weak decay constant f_πare 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_πand 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_πdeduced 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.

hep-ph↗

arXiv1996

Deriving the quark condensate within a finite Fermi system from the generating functional of chiral perturbation theory

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.

nucl-th↗

arXiv1996

Three disks in a row: A two-dimensional scattering analog of the double-well problem

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

chao-dyn↗

arXiv1996

Quantum Fluids and Classical Determinants

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.

chao-dyn↗

arXiv1996

Application of the diffraction trace formula to the three disk scattering system

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.

chao-dyn↗

arXiv1995

In-medium effective chiral lagrangians and the pion mass in nuclear matter

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)

hep-ph↗

arXiv1995

S-wave Meson-Nucleon Interactions and the Meson Mass in Nuclear Matter from Chiral Effective Lagrangians

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.

nucl-th↗

arXiv1994

Periodic Orbit Theory of Diffraction

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.

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