We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasiHermitian Hamiltonian are related to the symmetry generators of an equivalent Hermitian Hamiltonian. PACS number: 03.65.-w

We apply linear response theory to a general, inhomogeneous, stationary stellar system, with particular emphasis on dissipative processes analogous to Landau damping. Assuming only that the response is causal, we show that the irreversible work done by an external perturber is described by the anti-Hermitian part of a linear response operator, and damping of collective modes is described by the...

We apply linear response theory to a general, inhomogeneous, stationary stellar system, with particular emphasis on dissipative processes analogous to Landau damping. Assuming only that the response is causal, we show that the irreversible work done by an external perturber is described by the anti-Hermitian part of a linear response operator, and damping of collective modes is described by the...

We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator, and simplify the formula in terms of only the eigenvalues of the operator, using an ans...

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identi...

We define a sparse hermitian lattice Dirac matrix, H, coupling 2n+ 1 Dirac fermions. When 2n fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of H and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusi...

An Ad K invariant inner product on the Lie algebra of a compact connected Lie group K extends to a Hermitian inner product on the Lie algebra of the complexified Lie group Kc. The Laplace-Beltrami operator, ∆, on Kc induced by the Hermitian inner product determines, for each number a > 0, a Green’s function ra by means of the identity (a2−∆/4)−1 = ra∗. The Hilbert space of holomorphic functions...

We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η+, and η+-pseudo-Hermitian operators acting in C 2. The latter represent the physical observables of a model whose Hamiltonian and Hilbert space are respectively H and C2 endowed with the inner product defined by η+. Our calculations allows for a direct demonstration of the fact...

Abstract Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed a very serious problem during quantization. To cure this , we have considered properties of antilinearity that found inherently non-Hermitian Hamiltonians. Owing to existence antilinearity, construct an operator, called V -operator, which acts intertw...

Abstract It is shown that for a given hermitian Hamiltonian possessing supersymmetry, there is always a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for c...