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On the Courant-Fischer theory for Krein spaces

http://www.sciencedirect.com/science/article/B6V0R-4V462G8-2/2/25c16be9e99d2fbaa89b7c1a6a47e95f

Classes of non-Hermitian operators with real eigenvalues

The boundary of the Krein space tracial numerical range, an algebraic approach ...

In this article, tracial numerical ranges associated with matrices in an inde nite inner product space are investigated. The boundary equations of these sets are obtained and the case of the boundary being a polygon is studied. As an application, a numerical algorithm for plotting the tracial numerical range of an arbitrary complex matrix, is presented. Our approach uses the elementary idea that the boundary ma...

Flat portions on the boundary of the indefinite numerical range of 3×3 matrices

We focus on complex 3×3 matrices whose indefinite numerical ranges have a flat portion on the boundary. The results here obtained are parallel to those of Keeler, Rodman and Spitkovsky for the classical numerical range. ; http://www.sciencedirect.com/science/article/B6V0R-4S09585-1/1/cfd4cc3f5f7e4af2bc2e55b75b3a397b

Effects of eight-quark interactions on the hadronic vacuum and mass spectra of ...

The combined effective low energy QCD Lagrangians of Nambu-Jona-Lasinio (NJL) and 't Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant 't Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability con...

Dynamical chiral symmetry breaking by a magnetic field and multi-quark interact...

Catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions is considered. We use the three flavour Nambu-Jona-Lasinio type model with 't Hooft and eight-quark interaction terms. It is shown that the multi-quark interactions introduce new additional features to this phenomenon: (a) the local minimum of the effective potential catalyzed by the constant magnetic field is smoothed out...

Lowering the critical temperature with eight-quark interactions

It is shown that eight-quark interactions, which are needed to stabilize the ground state of the combined three flavor Nambu-Jona-Lasinio and 't Hooft Lagrangians, play also an important role in determining the critical temperature at which transitions occur from the dynamically broken chiral phase to the symmetric phase. ; http://www.sciencedirect.com/science/article/B6TVN-4MY0MF1-3/1/aafd91fae9368b31ad1a25...

Geometry of the numerical range of Krein space operators

The characteristic polynomial of the pencil generated by two J-Hermitian matrices is studied in connection with the numerical range. Geometric properties of the numerical range of linear operators on an inde nite inner product space are investigated. The point equation of the associated curve of the numerical range is derived, following Fiedler's approach for de nite inner product spaces. The classi cation of ...

Multi-quark interactions with a globally stable vacuum

It is shown that U(3)L×U(3)R eight-quark interactions stabilize the asymmetric ground state of the well-known model with four-quark Nambu-Jona-Lasinio and six-quark 't Hooft interactions. The result remains when the reduced SU(3) flavour symmetry is explicitly broken by the general current quark mass term with . ; http://www.sciencedirect.com/science/article/B6TVN-4J554P4-1/1/dfc257ebb68f9d0785afc0d0426a4516

Relativistic equation of state with short range correlations

Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The effect of the correlations in the ground state properties of the nuclear matter is studied.