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Normal ordering normal modes [PDF]
European Physical Journal C: Particles and Fields, 2021 In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have vanishing ...
Jarah Evslin
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Flow Equations and Normal Ordering [PDF]
Journal of Physics A: Mathematical and General, 2005 In this paper we consider flow-equations where we allow a normal ordering which is adjusted to the one-particle energy of the Hamiltonian. We show that this flow converges nearly always to the stable phase. Starting out from the symmetric Hamiltonian and
Elmar Körding +5 more
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Normal ordering of degenerate integral powers of number operator and its applications
Applied Mathematics in Science and Engineering, 2022 The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a ‘degenerate version’ of this, we consider the normal ordering of a degenerate integral
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Normal ordering associated with λ-Stirling numbers in λ-shift algebra
Demonstratio Mathematica, 2023 It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Complete normal ordering 1: Foundations [PDF]
Nuclear Physics B, 2016 We introduce a new prescription for quantising scalar field theories (in generic spacetime dimension and background) perturbatively around a true minimum of the full quantum effective action, which is to ‘complete normal order’ the bare action of ...
John Ellis +2 more
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Normal Order: Combinatorial Graphs [PDF]
Quantum Theory and Symmetries, 2003 A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators.
Blasiak, Pawel +4 more
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Deformed Bosons: Combinatorics of Normal Ordering [PDF]
European Physical Journal D, 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 combinatorial polynomials in the number operator N for which the generating functions and explicit ...
Pawel Blasiak, A Horzela, K A Penson
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Combinatorial solutions to normal ordering of bosons [PDF]
European Physical Journal D, 2005 Presented at 14th Int. Colloquium on Integrable Systems, Prague, Czech Republic, 16-18 June 2005.
Pawel Blasiak, A Horzela, K A Penson
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Walks, Partitions, and Normal Ordering [PDF]
The Electronic Journal of Combinatorics, 2015 We describe the relation between graph decompositions into walks and the normal ordering of differential operators in the $n$-th Weyl algebra. Under several specifications, we study new types of restricted set partitions, and a generalization of Stirling numbers, which we call the $\lambda$-Stirling numbers.
Askar Dzhumadil'daev, Damir Yeliussizov
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