International Journal of Modern Physics A

Reflections on spontaneous symmetry breaking, and the connection between condensed matter physics and particle physics, as given in a talk at a symposium at the University of Illinois in Urbana, celebrating the 50th anniversary of the theory of superconductivity.

We give an introductory review of quantum physics on the noncommutative space–time called the Groenewold–Moyal plane. Basic ideas like star products, twisted statistics, second quantized fields and discrete symmetries are discussed. We also outline some of the recent developments in these fields and mention where one can search for experimental signals.

We present a new realization of inverted neutrino mass hierarchy based on flavor symmetry. In this scenario, the deviation of the solar oscillation angle from π/4 is correlated with the value of θ₁₃, as they are both induced by a common mixing angle in the charged lepton sector. We find several interesting predictions: θ₁₃ ≥ 0.13, sin²θ₁₂ ≥ 0.31, sin²θ₂₃ ≃ 0.5 and 0 ≤ cos δ ≤ 0.7 for the neutrino oscillation parameters and 0.01 ≲ m_ββ ≲ 0.02 eV for the effective neutrino mass in neutrino-less double β-decay. We show that our scenario can also explain naturally the observed baryon asymmetry of the universe via resonant leptogenesis. The masses of the decaying right-handed neutrinos can be in the range (10³–10⁷) GeV, which would avoid the generic gravitino problem of supersymmetric models.

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what is most important, is that, at late times, the magnetic-induction contrast(δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

We study the consistency of the ladder approximation and the rainbow approximation of the Dyson–Schwinger equations of QCD. By considering the non-Abelian property of QCD, we show that the QED-type Ward–Takahashi identity is not required for the rainbow–ladder approximation of QCD. It indicates that there does not exist any internal inconsistency in the usual rainbow–ladder approximation of QCD. In addition, we propose a modified ladder approximation which guarantees the Slavnov–Taylor identity for the quark–gluon vertex omitting the ghost effect in the approximation.

The possibility of detecting neutrinos by coherent scattering on high Debye temperature monocrystals such as sapphire is presented and discussed. Preliminary estimations showed that 1 MeV neutrinos with a fluency density of 10¹² cm^-2 s^-1 could interact with a force of about 10^-6 dyn with a 100 g sapphire monocrystal. A torsion balance provided with 1 m length molybdenum wire and an optical autocollimator able to measure small rotation angles of about 0.1 arcsec could give positive results. The design of a high sensitivity torsion balance under construction provided with such a detector is presented and discussed.

We obtain constraints on possible structures of mass matrices in the quark sector by using as experimental restrictions the determined values of the quark masses at the M_Z energy scale, the magnitudes of the quark mixing matrix elements V_ud, V_us, V_cd and V_cs, and the Jarlskog invariant J(V). Different cases of specific mass matrices are examined in detail. The quality of the fits for the Fritzsch- and Stech-type mass matrices is about the same with χ²/d.o.f. = 4.23/3 = 1.41 and χ²/d.o.f. = 9.10/4 = 2.28, respectively. The fit for a simple generalization (one extra parameter) of the Fritzsch type matrices, in the physical basis, is much better with χ²/d.o.f. = 1.89/4 = 0.47. For comparison we also include the results using the quark masses at the 2 GeV energy scale. The fits obtained at this energy scale are similar to that at M_Z energy scale, implying that our results are unaffected by the evolution of the quark masses from 2 to 91 GeV.

Operational definition of space–time in light of quantum mechanics and general relativity inevitably indicates an intrinsic imprecision in space–time structure which has to do with space–time dimension as well. The operational dimension of space–time turns out to be a scale dependent quantity slightly smaller than four at distances ≫l_P. Close to the Planck length the deviation of space–time dimension from four becomes appreciable. The experimental bounds on the deviation of space–time dimension from four coming from the electron factor, Lamb shift in hydrogen atom and the perihelion shift in the planetary motion are still far from the theoretical predictions.

The Weyl–Wigner–Moyal formalism for Dirac second-class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this formalism, it is applied to the case of the relativistic free particle. Within this context, the Stratonovich–Weyl quantizer, Weyl correspondence, Moyal ⋆-product and Wigner function in the constrained phase-space are obtained. The recent Hamiltonian treatment for constrained systems, whose constraints depend explicitly on time, are used to perform the deformation quantization of the relativistic free charged particle in an arbitrary electromagnetic background. Finally, the system consisting of a charged particle interacting with a dynamical Maxwell field is quantized in this context.