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A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which…
We propose a simple model of two-dimensional N=2 superconformal mechanics with a spin-orbit interaction term and demonstrate that it inherits the Galilean symmetry of the initial free-particle system. We then propose a quaternionic…
A possible quantum-mechanical origin of statistical mechanics is discussed, and microcanonical and canonical ensembles of bosons and fermions are derived from the stationary Schr\"odinger equation in a unified manner. The interaction…
We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an…
We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac…
We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group $G$…
We introduce a new a family of $Z(N)$ multispins quantum chains with a free-fermionic ($N=2$) or free-parafermionic ($N>2$) eigenspectrum. The models have $(p+1)$ interacting spins ($p=1,2,\dots$), being Hermitian in the $Z(2)$ (Ising) case…
Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of…
We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane's…
Pseudo-Hermitian operators generalize the concept of Hermiticity. This class of operators includes the quasi-Hermitian operators, which reformulate quantum theory while retaining real-valued measurement outcomes and unitary time evolution.…
We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…
Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we…
Quantum field theory of space-like particles is investigated in the framework of absolute causality scheme preserving Lorentz symmetry. It is shown that tachyons are associated with unitary orbits of Poincar\'e mappings induced from SO(2)…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a…
We investigate the quantum properties of a non-random Hamiltonian with a step-like singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by…
A re-formulated, non-Hermitian version of the Witten's supersymmetric quantum mechanics is presented. Its use of pseudo-Hermitian (so called PT symmetric) Hamiltonians is reviewed and illustrated via several forms of an innovated…
We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac…
The permutation symmetry is a fundamental attribute of the collective wavefunction of indistinguishable particles. It makes a difference for the behavior of collective systems having different quantum statistics but existing in the same…
We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.
Scalar condensation, the well-established Higgs phenomenon, is the standard paradigm for building up renormalizable gauge-invariant theories of massive gauge bosons. In this short note, we demonstrate the uniqueness of the Higgs vacuum…