In this paper two kinds of two-boson realizations of the Higgs algebra are obtained by generalizing the well known Jordan-Schwinger realizations of the SU(2) and SU(1,1) algebras. In each kind, an unitary realization and two nonunitary realizations, together with the properties of their respective acting spaces are discussed in detail. Furthermore, similarity transformations, which connect the ...

The reconstruction of the unitary symmetry [1] under non-linear dynamical mapping Hilbert space of action amplitudes C onto projective Hilbert space CP (N−1) [2] has been applied here to the quantum dynamics of elementary vacuum excitations. The “vacuum manifold of virtual action states” is represented here by CP (N − 1) whereas its tangent vectors define local dynamical variables (LDV’s) descr...

We define an index for 2D G-invariant invertible states of bosonic lattice systems in the thermodynamic limit a finite symmetry group G with unitary action. show that this is invariant protected phase.

The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this c-duality are identified and they are placed in the context of Harish-Chandra’s legacy for the unitary representations program. Our paper begins with a discussion of path spac...

The SW(3/2, 3/2, 2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2)⊕su(2)⊕su(2) su(2) . At the central charge c = 10 2 the algebra coincides with the superconformal algebra associated to manifolds of G2 holonomy. The unitary minimal models of the ...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is n...

The concept of symmetry is of central importance in modern physics. Plenty information can be extracted from the symmetry of a physical system. In field theory, the symmetry plays an essential role in defining some very basic concept like particle, charge, etc. Symmetry also put strong constraint on the properties of fields/particles, as well as their interactions and correlations. In quantum f...

The algebra of generalized linear quantum canonical transformations is examined in the perspective of Schwinger’s unitary-canonical operator basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action-angle phase space formalism is established and it is shown that the conceptual foundation of the qu...

' N this paper we should like to call attention to certain approximate regularities among the square masses of the baryons with the hope that future research can establish whether they are real or are the result of numerical accidents in the limited data available. Our classification of states will be guided by the three-quark model of "baryons" and the principle of Regge recurrence. The states...