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Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
Various aspects of the Higgs boson phenomenology of the Minimal Supersymmetric Standard Model (MSSM) are reviewed. Emphasis is put on the effects of higher-order corrections. The masses and couplings are discussed in the MSSM with real and…
This is a continuation of the paper (quant-ph/0009012). In this letter we extend coherent operators and study some basic properties (the disentangling formula, resolution of unity, commutation relation, etc). We also propose a perspective…
The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and…
The formalism of quantum field theory in operator form, based on the anti self-adjoint operators of the imaginary coordinate and momentum and the self-adjoint operators of the real coordinate, momentum, energy and time, is used in…
This work prolongs recent investigations by Bergeron et al [see 2012 J. Phys. A: Math. Theo. 45 244028] on new SUSYQM coherent states for P\"oschl-Teller potentials. It mainly addresses explicit computations of eigenfunctions and spectrum…
We provide a non-linear realisation of composite Higgs models in the context of the SU(4)/Sp(4) symmetry breaking pattern, where the effective Lagrangian of the spin-0 and spin-1 resonances is constructed via the CCWZ prescription using the…
We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator.…
We employ the pinching theorem, ensuring that some operators A admit any sequence of contractions as an operator diagonal of A, to deduce/improve two recent theorems of Kennedy-Skoufranis and Loreaux-Weiss for conditional expectations onto…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
We explore the Higgs sector of the NMSSM in the limit when the Peccei--Quinn symmetry is exact or only slightly broken. In this case the Higgs spectrum has a hierarchical structure which is caused by the stability of the physical vacuum. We…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We consider one-loop amplitudes of a Higgs boson coupled to gluons in the limit of a large top quark mass. We treat the Higgs as the real part of a complex field phi that couples to the self-dual field strengths and compute the one-loop…
We examine a simple Composite Higgs Model (CHM) with vector resonances in addition to the Standard Model (SM) fields in perturbation theory by using the $K$-matrix method to implement unitarity constraints. We find that the $W_LW_L$…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
It is shown that some operators in quantum mechanics have hidden structures that are unobservable in principle. These structures are based on a supersymmetric decomposition of the momentum operator, and a nonassociative decomposition of the…
Following earlier studies, several new features of singular perturbation theory for one-dimensional quantum anharmonic oscillators are computed by exact WKB analysis; former results are thus validated.
We address some conjectures and open problems in "analysis of symmetries" which include the study of non-commutative harmonic analysis and discontinuous groups for reductive homogeneous spaces beyond the classical framework: (1) discrete…
We consider a massive particle of arbitrary spin and the basis vectors that carry the unitary, irreducible representations of the Poincar\'e group. From the complex coefficients in normalizable superpositions of these basis vectors, we…