No Arabic abstract
We study fermion-boson transitions. Our approach is based on the $3times 3$ subequations of Dirac and Duffin-Kemmer-Petiau equations, which link these equations. We demonstrate that free Dirac equation can be invertibly converted to spin-$0$ Duffin-Kemmer-Petiau equation in presence of a neutrino field. We also show that in special external fields, upon assuming again existence of a neutrino (Weyl) spinor, the Dirac equation can be transformed reversibly to spin-$0$ Duffin-Kemmer-Petiau equation. We argue that such boson-fermions transitions are consistent with the main channel of pion decay.
Thermodynamically, bosons and fermions differ by their statistics only. A general entropy functional is proposed by superposition of entropic terms, typical for different quantum gases. The statistical properties of the corresponding Janus particles are derived by variation of the weight of the boson/fermion fraction. It is shown that di-bosons and anti-fermions separate in gas and liquid phases, while three-phase equilibrium appears for poly-boson/fermion Janus particles.
In this work we consider a possible conceptual similarity between recent, amazing OPERA experiment of the superluminal propagation of neutrino and experiment of the gain-assisted superluminal light propagation realized about ten years ago. Last experiment refers on the propagation of the light, precisely laser pulse through a medium, precisely caesium atomic gas, with characteristic anomalous dispersion and corresponding negative group-velocity index with very large amplitude between two closely spaced gain lines (that is in some way similar to quantum theory of the ferromagnetism). It implies superluminal propagation of the light through this medium. Nevertheless all this, at it has been pointed out by authors, is not at odds with causality or special relativity, since it simply represents a direct consequence of the classical interference between ... different frequency components. We suggest that OPERA experiment can be in some way conceptually similar to the gain-assisted superluminal light propagation experiment. For this reason we suppose too that OPERA experiment can be simply explained in full agreement with causality and special relativity if there is some medium, precisely a scalar field (e.g. dark matter field, Higgs field or similar) through which neutrino propagates. We prove that, according to OPERA experiment data, supposed medium must be non-dispersive while its refractive index must be positive, smaller but relatively close to 1 (that is in some way similar to quantum theory of the diamagnetism). If it is true OPERA experiment results do not mean that special theory of relativity is broken, but they mean detection of suggested medium, i.e. a scalar field (e.g. dark matter field, Higgs field or similar).
Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). To work it out one needs definition of quantum Brownian motion. Since till very recent times only its boson version has been known, in present paper we demonstrate definition which makes possible consideration also for fermion Brownian motion.
The boson and fermion particle masses are calculated in a finite quantum field theory. The field theory satisfies Poincare invariance, unitarity and microscopic causality, and all loop graphs are finite to all orders of perturbation theory. The infinite derivative nonlocal field interactions are regularized with a mass (length) scale parameter $Lambda_i$. The $W$, $Z$ and Higgs boson masses are calculated from finite one-loop self-energy graphs. The $W^{pm}$ mass is predicted to be $M_W=80.05$ GeV, and the higher order radiative corrections to the Higgs boson mass $m_H=125$ GeV are damped out above the regulating mass scale parameter $Lambda_H=1.57$ TeV. The three generations of quark and lepton masses are calculated from finite one-loop self-interactions, and there is an exponential spacing in mass between the quarks and leptons.
One-loop radiative Majorana neutrino masses through the exchange of scalars have been considered for many years. We show for the first time how such a one-loop mass is also possible through the exchange of vector gauge bosons. It is based on a simple variation of a recently proposed $SU(2)_N$ extension of the standard model, where a vector boson is a candidate for the dark matter of the Universe.