Notes on Creation Operators
نویسنده
چکیده
Example 1 Let Bm = multiplication by the Schur function sm. The family {Bm} creates the homogeneous basis. Bm(sλ) is given by the Pieri rule. This implies that the homogeneous basis when expanded in terms of the Schur functions is given by bλ = ∑ μKμλsμ where the coefficients Kμλ are the column strict tableaux of shape μ and content λ. We could hope that a similar attack might work on more complicated bases (e.g. the Macdonald basis).
منابع مشابه
Creation and Annihilation Operators
Creation and annihilation operators are used in many-body quantum physics because they provide a less awkward notation than symmetrized or antisymmetrized wave functions, and a convenient language for perturbation theory, etc. These notes are not intended to give anything but an introduction. For a much more extended discussion see books on many-body theory, such as Fetter and Walecka, Quantum ...
متن کاملPDE from a probability point of view
These notes are for a course I gave while on sabbatical at UBC. It presupposes the reader is familiar with stochastic calculus; see the notes on my web page for Stochastic Calculus, for example. These notes for the most part are based on my book Diffusions and Elliptic Operators, Springer-Verlag, 1997. The topics covered are: stochastic differential equations, solving PDEs using probability, Ha...
متن کامل4 v 1 2 2 A ug 1 99 6 Eigenstates of linear combinations of two boson creation and annihilation operators : An algebraic approach
Eigenstates of the linear combinations a 2 + βa †2 and ab + βa † b † of two boson creation and annihilation operators are presented. The algebraic procedure given here is based on the work of Shanta et al. 1994] for constructing eigenstates of generalized annihilation operators.
متن کاملDiscrete Subgroups of the Poincaré Group
The framework of point form relativistic quantum mechanics is used to construct interacting four-momentum operators in terms of creation and annihilation operators of underlying constituents. It is shown how to write the creation and annihilation operators in terms of discrete momenta, arising from discrete subgroups of the Lorentz group, in such a way that the Poincaré commutation relations ar...
متن کاملDunkl Operators: Theory and Applications
These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform. We point out the connection with integrable particle systems of Calogero-MoserSut...
متن کامل