Related papers: On pseudo-Hermitian operators with generalized $\m…
A convexity theorem for certain G-orbits in a complexified Riemannian symmetric space G_C/K_C is proved. Applications to analytically continued spherical functions will be given.
We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying…
A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator…
A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $\lambda\in (-1,1)$. Within this…
We review some recent results of the so-called quasi-hermitian quantum mechanics, with particular focus on the quantum dynamics both in the Schr\"odinger and in the Heisenberg representations. The role of Krein spaces is also discussed.
A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum $\mathcal{PT}$-symmetric superintegrable models over an $n$-dimensional sphere $S^n$. The mechanism is illustrated with…
A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation.…
Non-Hermitian Hamiltonians H possess the real (i.e., observable) spectra inside certain specific domains of parameters D. In general, the determination of their observability-horizon boundaries is difficult. We list the pseudo-Hermitian…
In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras. In particular, we start with families of…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
The discussion in this study delves into Dirac's bra-ket formalism for a quasi-Hermitian quantum composite system based on the rigged Hilbert space (RHS). We establish an RHS with a positive definite metric suitable for a quasi-Hermite…
To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
In this note I generalize the classical results of Calabi-Vesentini to certain non-compact locally symmetric domains, namely those that are quotients of a hermitian symmetric domain by a neat arithmetic subgroup of the group of its…
We first investigate the geometry of orbits of the isotropy action on a semi-simple pseudo-Riemannian symmetric space by investigating the complexified action. Next we investigate the geometry of the orbits of Hermann type actions on the…
Non-Hermitian but P(phi)T(phi)-symmetrized spherically-separable Dirac and Schrodinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H(r), H(theta), and H(phi) play essential roles and offer some…
The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that the time evolution is…
We use a molecular characterization of generalized Hardy-Morrey spaces, to provide a norm controls of Calder\'on-Zygmund operators and their associated commutators in the above mention spaces.
Let $S(H)$ be the set of all self-adjoint bonded linear operators on $H$ and $\mathcal{V} \subset S(H)$ a subset that is pertinent in mathematical foundations of quantum mechanics. A symmetry is a bijective map $\phi :\mathcal{V} \to…