A new interpretation of the orthofermion algebra

Tekin, Ş C; Aydın, Fügen Torunbalcı; Arık, M.

doi:10.1088/1751-8113/40/27/018

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The Algebra ( ) and Its Relationship To The Orthofermion Alg1

Introduction1

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2009

2011

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Cited by 2 publications

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References 9 publications

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“…To prove this we exploit the fact that and are isomorphic which was shown in [20]. We know that the algebra is generated by 1 and a single pair of creation and annihilation operators * satisfying (4).…”

Section: The Algebra ( ) and Its Relationship To The Orthofermion Algmentioning

confidence: 99%

A q-deformed particle algebra with a unique d-dimensional representation

Tekin

Arık

2011

Open Physics

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Section: The Algebra ( ) and Its Relationship To The Orthofermion Algmentioning

confidence: 99%

A q-deformed particle algebra with a unique d-dimensional representation

Tekin

Arık

2011

Open Physics

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“…The algebra we call here "TAA algebra" was presented by Tekin, Aydin, and Arik in [14]. It is generated by an operator a and its adjoint a * .…”

Section: Introductionmentioning

confidence: 99%

Finite-dimensional calculus

Feinsilver¹,

Schott²

2009

J. Phys. A: Math. Theor.

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Abstract. We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".

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A new interpretation of the orthofermion algebra

Abstract: We present particle algebras whose representations correspond to states having at most p particles. For p = 1, the algebra corresponds to fermions. For p = 2, 3, 4, …, the algebra corresponds to the orthofermion algebra with a new interpretation.

Cited by 2 publications

References 9 publications

A q-deformed particle algebra with a unique d-dimensional representation

A q-deformed particle algebra with a unique d-dimensional representation

Finite-dimensional calculus

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