Related papers: PT-symmetry, ghosts, supersymmetry and Klein-Gordo…
Supersymmetry between bosons and fermions is modeled within PT- symmetric quantum mechanics. A non-Hermitian alternative to the Witten's supersymmetric quantum mechanics is obtained.
Extended quantum mechanics using non-Hermitian, pseudo-Hermitian Hamiltonians is briefly reviewed. Supersymmetric regularizations, solvable simulations and large-N expansion techniques are recollected as suitable means for the study of…
It is an interesting and open problem to trace the origin of the pseudospin symmetry in nuclear single-particle spectra and its symmetry breaking mechanism in actual nuclei. In this report, we mainly focus on our recent progress on this…
We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetry is a kind of fermionic…
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
Ghosts have been a stumbling block in the development of a UV complete quantum field theory for gravity. We discuss how difficulties associated with ghosts are overcome in the context of 0+1d QFT. Obtaining a probability interpretation is…
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…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a previously unnoticed symmetry, which is present for any Lagrangian term that involves $\dot{x}^2$. As a basic model that incorporates…
A review of new aspects concerning time-symmetry in Quantum Mechanics.
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
Quantum systems governed by non-Hermitian Hamiltonians with $\PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We argue that $\PT$ symmetry may also be important and present at the level…
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…
Nuclear supersymmetry is reviewed and some of its applications and extensions are discussed, together with a proposal for new, more stringent and precise tests to probe the supersymmetry classification, in particular, correlations between…
Supersymmetry, a new symmetry that relates bosons and fermions in particle physics, still escapes observation. Search for supersymmetry is one of the main aims of the Large Hadron Collider. The other possible manifestation of supersymmetry…
Position and momentum enter at the same level of importance in the formulation of classical or quantum mechanics. This is reflected in the invariance of Poisson brackets or quantum commutators under canonical transformations, which I regard…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…