Heisenberg algebra , anyons and d = 2 + 1 supersymmetry
نویسنده
چکیده
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized to some d = 2 + 1 supersymmetric field systems. Quadratic and linear forms of action functionals are found for the universal minimal as well as for supersymmetric spinor sets of equations. A possibility of constructing a universal classical mechanical model for d = 2 + 1 spin systems is discussed.
منابع مشابه
R-deformed Heisenberg algebra
It is shown that the deformed Heisenberg algebra involving the reflection operator R (Rdeformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special differentiation operator. Guon-like form of the algebra, related to the generalized statistics, is found. Some applications of revealed representations of the R-d...
متن کاملar X iv : h ep - t h / 97 05 04 3 v 1 7 M ay 1 99 7 Universality of the R - deformed Heisenberg algebra ∗
We show that deformed Heisenberg algebra with reflection emerging in parabosonic constructions is also related to parafermions. This universality is discussed in different algebraic aspects and is employed for the description of spin-j fields, anyons and supersymmetry in 2+1 dimensions.
متن کاملDeformed Heisenberg Algebra, Fractional Spin Fields and Supersymmetry without Fermions
Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), [a, a] = 1+ νK, involving the Klein operator K, {K, a±} = 0, K = 1. The connection of the minimal set of equations with the earlier proposed ‘universal’...
متن کاملUniversidade Federal de Juiz de Fora
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized to some d = 2 + 1 supersymmetric field systems. Quadratic and linear forms of action functionals are found for the universal minimal as well as for supersym...
متن کاملInteracting anyons in topological quantum liquids: the golden chain.
We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical wit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997