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CRC Press eBooks

CREATION AND ANNIHILATION OPERATORS

Richard P. Feynman

Published Mar 9, 2018• 28 citations
Publisher

Abstract

In this chapter we shall describe an operator formalism that has widespread applications in quantum mechanics, notably in dealing with harmonic oscillators and in describing many-particle systems.
DOI
10.1201/9780429493034-6

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It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.