Seesaw, coherence and neutrino oscillations

We present a prescription for consistently constructing non-Fock coherent flavour neutrino states within the framework of the seesaw mechanism, and establish that the physical vacuum of massive neutrinos is a condensate of Standard Model massless neutrino states. The coherent states, involving a finite number of massive states, are derived by constructing their creation operator. This construction fulfills automatically the key requirement of coherence for the oscillations of particles to occur. We comment on the inherent non-unitarity of the oscillation probability induced by the requirement of coherence.

Monopole and instanton effects in QCD

We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) the monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) the decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.

Vertex operators, t-boson model and weighted plane partitions in finite boxes

We consider two different subjects: the algebra of Hall–Littlewood functions and t-boson model. Tsilevich and Sułkowski, respectively, give that the creation operator [Formula: see text] in the monodromy matrix of t-boson model can be represented by [Formula: see text], where [Formula: see text] and [Formula: see text] are vertex operators closely related to the Hall–Littlewood functions. In this paper, we obtain that the annihilation operator [Formula: see text] in the monodromy matrix and other relations of t-boson model can also be realized in the algebra of Hall–Littlewood functions. Meanwhile, we get that the generating functions of weighted plane partitions in finite boxes can be obtained from the operators [Formula: see text].

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many particle-many hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number [Formula: see text] and, numerically, for [Formula: see text]. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

On the deformed photon-added and photon-subtracted states

In this paper, we introduce the deformed algebra whose number operator is expressed in terms of the product of the creation operator and annihilation operator. We give some examples for these kinds of deformed algebras. For Arik–Coon's q-oscillator algebra, we discuss, especially, the photon-added states and the photon-subtracted states and construct their associated generation functions.