ترغب بنشر مسار تعليمي؟ اضغط هنا

Approximate substitutions and the normal ordering problem

61   0   0.0 ( 0 )
 نشر من قبل Gerard Henry Edmond Duchamp
 تاريخ النشر 2008
والبحث باللغة English
 تأليف H. Cheballah




اسأل ChatGPT حول البحث

In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations.

قيم البحث

اقرأ أيضاً

84 - P Blasiak 2005
We solve the boson normal ordering problem for (q(a*)a + v(a*))^n 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 representation to the exponential generating functions of Sheffer-type polynomials. This in turn opens a vast arena of combinatorial methodology which is applied to boson normal ordering and illustrated by a few examples.
102 - P. Blasiak 2007
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling numbers e numerating partitions of a set. This framework reveals several inherent relations between ordering problems and combinatorial objects, and displays the analytical background to Wicks theorem. The methodology can be straightforwardly generalized from the simple example given herein to a wide class of operators.
76 - K A Penson 2005
We solve the boson normal ordering problem for $(q(a^dag)a+v(a^dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^dag$ are boson annihilation and creation operators, satisfying $[a,a^dag]=1$. This consequently provi des the solution for the exponential $e^{lambda(q(a^dag)a+v(a^dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.
124 - G. H. E. Duchamp 2008
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that i n this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced.
85 - P. Blasiak 2004
We solve the normal ordering problem for (A* A)^n where A* (resp. A) are one mode deformed bosonic creation (resp. annihilation) operators satisfying [A,A*]=[N+1]-[N]. The solution generalizes results known for canonical and q-bosons. It involves com binatorial polynomials in the number operator N for which the generating functions and explicit expressions are found. Simple deformations provide examples of the method.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا