N‐Body Bose System with a Finite Number of States. I. Irreducible Representations

Autor:	Joseph B. Aviles
Rok vydání:	1963
Předmět:	Pure mathematics Differential equation Statistical and Nonlinear Physics Elementary particle Second quantization Combinatorics Many-body problem symbols.namesake Irreducible representation symbols Hamiltonian (quantum mechanics) Finite set Mathematical Physics Mathematics Boson
Zdroj:	Journal of Mathematical Physics. 4:473-483
ISSN:	1089-7658 0022-2488
DOI:	10.1063/1.1703979
Popis:	For the purpose of investigating the N‐Body Bose System with a finite number of states, we analyze Xij = Ai†Aj, i, j ≤ K. (A and A† are the usual annihilation and creation operators of the second quantization formalism). The Hamiltonian for a fixed number of particles may be expressed in terms of the (finite‐dimensional) irreducible representations of the Xij. A set of fundamental equations is defined for the irreducible representations Xij(N, K), i, j ≤ K and is solved for arbitrary N and K. The analysis of the structure of the Xij(N, K) yields a simple, systematic method for listing all possible ways in which n1+ … ni+ … + nK = N may be satisfied for ni positive integral or zero. This leads to a particularly simple method for constructing the Xij(N, K), i, j ≤ K.
Databáze:	OpenAIRE
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