19 research outputs found
Para-Grassmann Variables and Coherent States
The definitions of para-Grassmann variables and q-oscillator algebras are
recalled. Some new properties are given. We then introduce appropriate coherent
states as well as their dual states. This allows us to obtain a formula for the
trace of a operator expressed as a function of the creation and annihilation
operators.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Para-Grassmann variables and coherent states
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a operator expressed as a function of the creation and annihilation operators.Facultad de Ciencias Exacta
A note on Gaussian integrals over para-Grassmann variables
We discuss the generalization of the connection between the determinant of an operator entering a quadratic form and the associated Gaussian path-integral valid for Grassmann variables to the para-Grassmann case [θp+1 = 0 with p = 1 (p > 1) for Grassmann (para-Grassmann) variables]. We show that the q-deformed commutation relations of the para-Grassmann variables lead naturally to consider q-deformed quadratic forms related to multiparametric deformations of GL(n) and their corresponding q-determinants. We suggest a possible application to the study of disordered systems.Facultad de Ciencias Exacta
On Linear Differential Equations Involving a Para-Grassmann Variable
As a first step towards a theory of differential equations involving
para-Grassmann variables the linear equations with constant coefficients are
discussed and solutions for equations of low order are given explicitly. A
connection to n-generalized Fibonacci numbers is established. Several other
classes of differential equations (systems of first order, equations with
variable coefficients, nonlinear equations) are also considered and the
analogies or differences to the usual (''bosonic'') differential equations
discussed
Para-Grassmann variables and coherent states
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a operator expressed as a function of the creation and annihilation operators
Para-Grassmann variables and coherent states
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a operator expressed as a function of the creation and annihilation operators.Facultad de Ciencias Exacta
Nonlinear Fermions and Coherent States
Nonlinear fermions of degree (-fermions) are introduced as particles
with creation and annihilation operators obeying the simple nonlinear
anticommutation relation . The
()-order nilpotency of these operators follows from the existence of
unique -vacuum. Supposing appropreate ()-order nilpotent para-Grassmann
variables and integration rules the sets of -fermion number states, 'right'
and 'left' ladder operator coherent states (CS) and displacement-operator-like
CS are constructed. The matrix realization of the related
para-Grassmann algebra is provided. General -order nilpotent ladder
operators of finite dimensional systems are expressed as polynomials in terms
of -fermion operators. Overcomplete sets of (normalized) 'right' and 'left'
eigenstates of such general ladder operators are constructed and their
properties briefly discussed.Comment: latex, 16 pages, no figure
Para-Generalization of Peierls Bracket Quantization
A convenient formalism is developed to treat classical dynamical systems
involving parafermionic and parabosonic dynamical variables. This is
achieved via the introduction of a parabracket which summarizes the
paracommutation relations of the corresponding Green components in a unified
manner. Furthermore, it is shown that Peierls quantization scheme may be
applied to such systems provided that one uses the above mentioned parabracket
to express the quantum paracommutation relations. Application of the Peierls
scheme also provides the form of the parafermionic and parabosonic kinetic
terms in the Lagrangian.Comment: LaTeX file, 27 pages
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems
In this paper, we investigate the entanglement of multi-partite Grassmannian
coherent states (GCSs) described by Grassmann numbers for degree of
nilpotency. Choosing an appropriate weight function, we show that it is
possible to construct some well-known entangled pure states, consisting of {\bf
GHZ}, {\bf W}, Bell, cluster type and bi-separable states, which are obtained
by integrating over tensor product of GCSs. It is shown that for three level
systems, the Grassmann creation and annihilation operators and
together with form a closed deformed algebra, i.e., with
, which is useful to construct entangled qutrit-states.
The same argument holds for three level squeezed states. Moreover combining the
Grassmann and bosonic coherent states we construct maximal entangled super
coherent states