Coherent states for bosons and fermions

Robert Gilmore, D.H. Feng

R. Shankar

Mohammed Daoud A, M. Kibler

We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and a k-fermion leads to a definition of fractional supercoherent states. Such states involve bosonic coherent states and k-fermionic coherent states. We construct an Hamiltonian which generalizes the ordinary (or Z_2-graded) supersymmetric oscillator Hamiltonian. Our Hamiltonian describes a fractional (or Z_k-graded) supersymmetric oscillator for which the fractional supercoherent states are coherent states.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Tomáš Tyc, Brett Hamilton, Barry C. Sanders +1 more

Whereas boson coherent states provide an elegant, intuitive and useful representation, we show that the desirable features of boson coherent states do not carry over very well to fermion fields unless one is prepared to use exotic approaches such as Grassmann fields. Specifically, we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that fermion coherent states, and approximations to fermion coherent states, defined over the complex field, do not behave well for any of these four criteria.

Mohammed Daoud A, Y. Hassouni, M. Kibler

A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.