Casimir Effect for Fermion Condensate in Conical Rings

The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the period equal to the flux quantum. Depending on the boundary conditions, the condensate can be either positive or negative. For a massless field the FC in the boundary-free conical geometry vanishes and the nonzero contributions are purely edge-induced effects. This provides a mechanism for time-reversal symmetry breaking in the absence of magnetic fields. Combining the results for the fields corresponding to two inequivalent irreducible representations of the Clifford algebra, the FC is investigated in the parity and time-reversal symmetric fermionic models and applications are discussed for graphitic cones.

CHIRAL AND U(1)A RESTORATIONS HIGH IN THE HADRON SPECTRUM, SEMICLASSICAL APPROXIMATION AND LARGE Nc

In quantum systems with large n (radial quantum number) or large angular momentum the semiclassical (WKB) approximation is valid. A physical content of the semiclassical approximation is that the quantum fluctuations effects are suppressed and vanish asymptotically. The chiral as well as U (1)A breakings in QCD result from quantum fluctuations. Hence these breakings must be suppressed high in the spectrum and the spectrum of high-lying hadrons must exhibit U (2)L × U (2)R symmetry of the classical QCD Lagrangian. This argument can be made stronger for mesons in the large Nc limit. In this limit all mesons are stable against strong decays and the spectrum is infinite. Hence, one can excite mesons of arbitrary large size with arbitrary large action, in which case the semiclassical limit is manifest. Actually we do not need the exact Nc = ∞ limit. For any large action there always exist such Nc that the isolated mesons with such an action do exist and can be described semiclassically. From the empirical fact that we observe multiplets of chiral and U (1)A groups high in the hadron spectrum it follows that Nc = 3 is large enough for this purpose.

SECTOR OF THE 2++ MESONS: OBSERVATION OF THE TENSOR GLUEBALL

Data of the Crystal Barrel and L3 collaborations clarified essentially the situation in the 2++ sector in the mass region up to 2400 MeV, demonstrating the linearity of (n, M2) trajectories, where n is the radial quantum number of a quark–antiquark state with mass M. We discuss these data and show that there exists a superfluous state for the (n, M2) trajectories: a broad resonance f2(2000). We pay special attention to the reactions [Formula: see text] in the mass region 1990–2400 MeV where, together with f2(2000), four relatively narrow resonances are seen: f2(1920), f2(2020), f2(2240), f2(2300). We analyze the branching ratios of all these resonances and show that only the decay couplings of the broad state f2(2000) → π0π0, ηη, ηη′ satisfy relations inherent in the glueball decay.