Relativistic Corrections in a Three-Boson System of Equal Masses

Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the mass-shell constraints can be reduced to a three-dimensional eigenvalue problem. In general, this problem is complicated, but for three equal masses a drastic simplification arises at the first post-Galilean order: the reduced wave equation becomes tractable, and we can compute a first-order correction beyond the nonrelativistic limit. The harmonic interaction is displayed as a toy model.Comment: 16 pages, no figure. Several points clarified, one typo corrected. References added. To appear in Physical Review

Strong Interactions at Low Energy

The lectures review some of the basic concepts relevant for an understanding of the low energy properties of the strong interactions: chiral symmetry, spontaneous symmetry breakdown, Goldstone bosons, quark condensate. The effective field theory used to analyze the low energy structure is briefly sketched. As an illustration, I discuss the implications of the recent data on the decay $K\to \pi\pi e\nu$ for the magnitude of the quark condensate.Comment: Lectures given at the school of physics "Understanding the structure of hadrons", Prague, July 2001, 20 p

Chiral Perturbation Theory for the Quenched Approximation of QCD

[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.Comment: 14 page

Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.Comment: 7pages, LaTeX2

The Goldberger -- Treiman Relation, gAg_A and gπNNg_{\pi NN} at T≠0T\neq 0

The Goldberger-Treiman relation is shown to persist in the chiral limit at finite temperatures to order $O(T^2)$. The $T$ dependence of $g_A$ turns out to be the same as for $F_{\pi}$, $g_{A}(T)=g_{A}(0)(1-T^2/12F^2)$, while $g_{\pi NN}$ is temperature independent to this order. The baryon octet ${\cal D}$ and ${\cal F}$ couplings also behave as $F_{\pi}$ if only pions are massless in the pseudoscalar meson octet.Comment: 7p, NSF-ITP-93-145, BUTP-93/27, PUTP-1433, November 199

Quantum Fluctuations of a Coulomb potential

Long-range properties of the two-point correlation function of the electromagnetic field produced by an elementary particle are investigated. Using the Schwinger-Keldysh formalism it is shown that this function is finite in the coincidence limit outside the region of particle localization. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly, and its gauge independence is proved. The leading contribution turns out to be of zero order in the Planck constant, and the relative value of the root mean square fluctuation of the Coulomb potential is found to be 1/\sqrt{2}, confirming the result obtained previously within the S-matrix approach. It is shown also that in the case of a macroscopic body, the \hbar^0 part of the correlation function is suppressed by a factor 1/N, where N is the number of particles in the body. Relation of the obtained results to the problem of measurability of the electromagnetic field is mentioned.Comment: 15 pages, 2 figure

U(3) chiral perturbation theory with infrared regularization

We include the eta-prime in chiral perturbation theory without employing 1/N_c counting rules. The method is illustrated by calculating the masses and decay constants of the Goldstone boson octet (pions, kaons, eta) and the singlet eta-prime up to one-loop order. The effective Lagrangian describing the interactions of the eta-prime with the Goldstone boson octet is presented up to fourth chiral order and the loop integrals are evaluated using infrared regularization, which preserves Lorentz and chiral symmetry.Comment: 29 page

The structure functions of longitudinal virtual photon at low virtualities

The structure functions of longitudinal virtual photon at low virtualities are calculated in the framework of chiral pertubation theory(ChPT) in the zero and first order of ChPT. It is assumed that the virtuality of target longitudinal photon is much less than the virtuality of the hard projectile photon and both are less than the characteristic ChPT scale.Comment: 16 pages, 8 figure

Next-to-leading-order temperature corrections to correlators in QCD

Corrections of order $T^4$ to vector and axial current correlators in QCD at a finite temperature $T<T_c$ are obtained using dispersion relations for the amplitudes of deep inelastic scattering on pions. Their relation with the operator product expansion is presented. An interpretation of the results in terms of $T$-dependent meson masses is given: masses of $\rho$ and $a_1$ start to move with temperature in order $T^4$.Comment: 13 pages, no figures, CERN-TH.7215/94, BUTP-94/

A low energy theory for superfluid and solid matter and its application to the neutron star crust

We formulate a low energy effective theory describing phases of matter that are both solid and superfluid. These systems simultaneously break translational symmetry and the phase symmetry associated with particle number. The symmetries restrict the combinations of terms that can appear in the effective action and the lowest order terms featuring equal number of derivatives and Goldstone fields are completely specified by the thermodynamic free energy, or equivalently by the long-wavelength limit of static correlation functions in the ground state. We show that the underlying interaction between particles that constitute the lattice and the superfluid gives rise to entrainment, and mixing between the Goldstone modes. As a concrete example we discuss the low energy theory for the inner crust of a neutron star, where a lattice of ionized nuclei coexists with a neutron superfluid.Comment: 21 pages, 1 figur