A generalization of boson normal ordering
نویسندگان
چکیده
In this Letter we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to shed further light onto the combinatorics arising from algebraic and Fock space properties of boson operators. © 2006 Elsevier B.V. All rights reserved.
منابع مشابه
Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem
We consider the numbers arising in the problem of normal ordering of expressions in boson creation a† and annihilation a operators a ,a† =1 . We treat a general form of a boson string a† rnasn . . . a† r2as2 a† r1as1 which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions Dobiński-type formulas are obtained for thes...
متن کاملBoson Normal Ordering via Substitutions and Sheffer-type Polynomials
We solve the boson normal ordering problem for (q(a)a + v(a)) with arbitrary functions q and v and integer n, where a and a are boson annihilation and creation operators, satisfying [a, a] = 1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state ...
متن کاملar X iv : q ua nt - p h / 05 10 08 2 v 1 1 2 O ct 2 00 5 Combinatorial Solutions to Normal Ordering of Bosons
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions-the Stirling and Bell numbers, Bell polynomials and Dobi´nski relations-lead to calculational tools which allow to find explicitly normally ordered forms for a large class of operator functions. 1 Preface Solutions to mathematical problems whic...
متن کاملDobiński relations and ordering of boson operators
We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical...
متن کاملOn the Normal Ordering of Multi-mode Boson Operators
In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the corresponding problem of the single-mode case. To describe the normal ordering in the multi-mode case for each mode a colour is introduced and coloured contrac...
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 2006