A Bose description of the 1-D para-Bose and para-Fermi oscillators

In the Fock space of two Bose operators all the irreducible representations of both the 1-D para-Bose and para-Fermi oscillators are constructed. Bose states of the form |p + k–1, kn > (|p – k, kn), n = 1,2, are shown to stand for states of k-parabosons (k-parafermions) of order p. For n = 1 or n = 2 the various subspaces may be visualized in the plane as either straight-lines or parabolae, respectively.

ORDINARY DIFFERENTIAL EQUATIONS, FIRST INTEGRALS, CONFORMAL INVARIANTS, BOSE OPERATORS, COHERENT STATES AND ENTANGLEMENT

Autonomous systems of first order ordinary differential equations can be embedded into a Hilbert space description by using Bose operators and Glauber coherent states. The first integrals and conformal invariants of the autonomous system can be represented by states in a Hilbert space. Thus the embedding in a Hilbert space allows us to study entanglement of the states. We apply it here to first integrals and conformal invariants which are expressed as states.

A KIND OF NONLINEAR COHERENT-ENTANGLED STATE AND SQUEEZING PROPERTY

Based on the technique of integration within an ordered product of nonlinear Bose operators, a new kind of nonlinear coherent entangled state, which exhibits both the property of coherent state and quantum entanglement, is constructed and its application in squeezing is discussed.