Magnetic Oscillations in the Nambu - Jona-Lasinio model

The phase structure of a simple Nambu-Jona-Lasinio model has been investigated at non-zero values of $\mu$ and H, where H is an external magnetic field and $\mu$ is the chemical potential. On this basis magnetic oscillations effects were considered. It was shown that there are standard (periodic) van Alphen-de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density in the NJL system. Besides, we have found non-standard, i.e. non-periodic, magnetic oscillations, since the frequency of oscillations is a H-dependent quantity. Finally, there arises an oscillating behaviour not only for thermodynamical quantities, but also for a dynamical quantity like the quark mass. The possibility for magnetic oscillations of some physical quantities inside neutron stars is discussed.Comment: RevTeX, 12 pages; Talk given by K.G. Klimenko at the International Workshop on Hadron Physics, 10-15 September 1999, Coimbra, Portuga

Diquarks in the color--flavor locked phase of dense quark matter

Diquark excitations of dense quark matter are considered in the framework of the Nambu -- Jona-Lasinio model with three types of massless quarks in the presense of a quark number chemical potential $\mu$. We investigate the effective action of meson- and diquark fields at sufficiently high values of $\mu$, where the color--flavor locked (CFL) phase is realized, and prove the existence of NG-bosons in the sector of pseudoscalar diquarks. In the sector of scalar diquarks an additional NG-boson is found, corresponding to the spontaneous breaking of the U(1)$_B$ baryon symmetry in the CFL phase. Finally, the existence of massive scalar and pseudoscalar diquark excitations is demonstrated.Comment: 10 pages, 2 figures; version accepted for publication in PR

An alternative construction of B-M and B-T unitals in Desarguesian planes

We present a new construction of non-classical unitals from a classical unital $U$ in $PG(2,q^2)$. The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model $\Pi$ of $PG(2,q^2)$ with the following three properties: 1. points of $\Pi$ are those of $PG(2,q^2)$; 2. lines of $\Pi$ are certain lines and conics of $PG(2,q^2)$; 3. the points in $U$ form a non-classical B-M unital in $\Pi$. Our construction also works for the B-T unital, provided that conics are replaced by certain algebraic curves of higher degree.Comment: Keywords: unital, desarguesian plane 11 pages; ISSN: 0012-365

Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space

We study the dynamical breaking of chiral and color symmetries of dense quark matter in the ultrastatic hyperbolic spacetime $R\otimes H^3$ in the framework of an extended Nambu--Jona-Lasinio model. On the basis of analytical expressions for chiral and color condensates as functions of curvature and temperature, the phenomenon of dimensional reduction and gravitational catalysis of symmetry breaking in strong gravitational field is demonstrated in the regime of weak coupling constants. In the case of strong couplings it is shown that curvature leads to small corrections to the flat-space values of condensate and thus enhances the symmetry breaking effects. Finally, using numerical calculations phase transitions under the influence of chemical potential and negative curvature are considered and the phase portrait of the system is constructed.Comment: 14 pages, 5 figure

The Momentum--Space Bosonization of the Nambu--Jona-Lasinio Model with Vector and Axial-Vector Mesons

The momentum-space bosonization method is extended to the case of a Nambu--Jona-Lasinio type model with vector and axial-vector mesons. The method presented gives the possibility of deriving any meson vertex function to all orders in momenta and to the leading order in $1/N_c$. Two-point functions, which describe one-particle transitions to the hadronic vacuum, and meson self-energies are considered. We find new relations which generalize the well-known KSFR relation and both the first and the second Weinberg sum rules. These result from a consistent treatment of higher order terms in the momentum expansion.Comment: 11pp, TeX, CRN 93-5