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A.J. Macfarlane

Researcher at University of Cambridge

Publications -  66
Citations -  2616

A.J. Macfarlane is an academic researcher from University of Cambridge. The author has contributed to research in topics: Supersymmetry & Lie algebra. The author has an hindex of 19, co-authored 66 publications receiving 2560 citations.

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On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q

TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.
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Invariant tensors for simple groups

TL;DR: In this paper, a new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology, and relations involving the d and f su(n) tensors are given.
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Generalised harmonic oscillator systems and their Fock space description

TL;DR: In this paper, a generalisation of the quantum harmonic oscillator, which involves a deformation parameter q and a modification parameter ν, and its Fock space Fq,ν, is described.
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Group theoretical foundations of fractional supersymmetry

TL;DR: In this article, it is shown that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group.
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New supersymmetry of the monopole

TL;DR: In this paper, the geometrical origin of this supersymmetry is traced, and its relationship with the constrained dynamics of a spinning particle on a sphere centered at the monopole is described.