The Friedrichs extension and the Krein extension of a positive operator in a Krein space are characterized in terms of their spectral functions in a Krein space.

The helicity amplitudes of the electroexcitation of the Roper resonance on proton are extracted at 1.7 < Q < 4.2 GeV 2 from recent high precision JLab-CLAS cross sections data and longitudinally polarized beam asymmetry for π electroproduction on protons. The analysis is made using two approaches, dispersion relations and unitary isobar model, which give consistent results. It is found that the...

It was previously shown by one of us that in any static, nonglobally-hyperbolic, spacetime it is always possible to define a sensible dynamics for a Klein-Gordon scalar field. The prescription proposed for doing so involved viewing the spatial derivative part, A, of the wave operator as an operator on a certain L Hilbert space H and then defining a positive, self-adjoint operator on H by taking...

This paper offers the functional model of a class of non-selfadjoint extensions of a Hermitian operator with equal deficiency indices. The explicit form of dilation of a dissipative extension is offered and the symmetric form of Sz.Nagy-Foiaş model as developed by B. Pavlov is constructed. A variant of functional model for a general non-selfadjoint non-dissipative extension is formulated. We il...

In the excited baryon spectrum, of particular interest is the level order of the positive-parity excited nucleon, so-called the Roper resonance N (1440) and the negative-parity nucleon N(1535). It is worth mentioning that this pattern of the level order between positive and negative-parity excited states can be found universally in the ∆, Σ and flavor-octet Λ channels. It is also interesting to...

We discuss a new description for the Roper resonance, the first nucleon excited state of JP = 1/2+, in a model of strong diquark correlations. Treating the scalarisoscalar and axial-vector–isovector diquarks as independent degrees of freedom, two states having nucleon quantum numbers are constructed. Due to the scalar and axial-vector nature of the diquarks, the two nucleon states have differen...

We study excited states of the nucleon in quenched lattice QCD with the spectral analysis using the maximum entropy method. Our simulations are performed on three lattice sizes 16 × 32, 24 × 32 and 32 × 32, at β = 6.0 to address the finite volume issue. We find a significant finite volume effect on the mass of the Roper resonance for light quark masses. After removing this systematic error, its...