International Journal of Modern Physics A

The recent evidence for neutrino oscillations stimulate us to discuss again the problem of fermion masses and mixings in gauge theories. In the standard model, several forms for quark mass matrices are equivalent. They become ansatze within most extensions of the standard model, where also relations between quark and lepton sectors may hold. In a seesaw framework, these relations can constrain the scale of heavy neutrino mass, which is often related to the scale of intermediate or unification gauge symmetry. As a consequence, two main scenarios arise. Hierarchies of masses and mixings may be explained by broken horizontal symmetries.

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator ρ(0) and the projection operator E(t) = U(t) EU^†(t) is measured continuously from t = 0 to T, where E is a projector obeying Eρ(0)E = ρ(0) and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. Then the probability of always finding E(t) = 1 from t = 0 to T is unity. Generically E(T) ≠ E and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.

In this work, constraint conversion techniques are used to disclose the role of the second-class constraints as generator of hidden symmetries. The example of the SU(2) Skyrme model is thoroughly investigated in this approach. This study is generalized to a set of second-class surfaces of arbitrary geometries resulting from the semiclassical quantization of the collective mode of nonlinear field theories. The consequences of the hidden symmetry over the physical spectrum and the ordering ambiguity problem are explored.

Starting from the classification of real Manin triples we look for those that are isomorphic as six-dimensional Drinfeld doubles i.e. Lie algebras with the ad-invariant form used for construction of the Manin triples. We use several invariants of the Lie algebras to distinguish the nonisomorphic structures and give the explicit form of maps between Manin triples that are decompositions of isomorphic Drinfeld doubles. The result is a complete list of six-dimensional real Drinfeld doubles. It consists of 22 classes of nonisomorphic Drinfeld doubles.

We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3,4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger–Dyson equations can be completely reproduced through purely geometrical consideration. From this result, we speculate that all heterogeneous loop amplitudes can be derived from the geometrical consideration and the consistency among relevant amplitudes.

The eigenstates and their degeneracy for parasupersymmetric Hamiltonian of arbitrary order p, corresponding to the motion of a charged particle with spin on the flat surface in the presence of a constant magnetic field along z-axis, are calculated. The eigenstates are expressed in terms of Landau levels quantum states with dynamical symmetry group H₄. Furthermore, parasupersymmetric coherent states with multiplicity degeneracy are derived for an ad hoc lowering operator of the eigenstates in terms of ordinary coherent states of Landau Hamiltonian.

For many systems with second-class constraints, the question posed in the title is answered in the negative. We prove this for a range of systems with two second-class constraints. After looking at two examples, we consider a fairly general proof. It is shown that, to unravel gauge invariances in second-class constrained systems, it is sufficient to work in the original phase space itself. Extension of the phase space by introducing new variables or fields is not required.

A simple method to compute QED bound state properties is presented, in which binding energy effects are treated nonperturbatively. It is shown that to take the effects of all ladder Coulomb photon exchanges into account, one can simply perform the derivative of standard QED amplitudes with respect to the external momentum. For example, the derivative of the light-by-light scattering amplitude gives an amplitude for orthopositronium decay to three photons where any number of Coulomb photon exchanges between the e⁺e^- is included.

Various applications are presented. From them, it is shown that binding energy must be treated nonperturbatively in order to preserve the analyticity of positronium decay amplitudes.

Interesting perspectives for quarkonium physics are briefly sketched.

We study the production and signatures of heavy exotic quarks pairs at LHC in the framework of the vector singlet model (VSM), vector doublet model (VDM) and fermion-mirror-fermion (FMF) model. The pair production cross-sections for the electroweak and strong sector are computed.