REVIEW 2 cited by
Graded colour Lie superalgebras for solving L\'evy-Leblond equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
The L\'evy-Leblond equation with free potential admits a symmetry algebra that is a $ \mathbb{Z}_2\times\mathbb{Z}_2 $-graded colour Lie superalgebra (see arXiv:1609.08224). We extend this result in two directions by considering a time-independent version of the L\'evy-Leblond equation. First, we construct a $ \mathbb{Z}_2^3 $-graded colour Lie superalgebra containing operators that leave the eigenspaces invariant and demonstrate the utility of this algebra in constructing general solutions for the free equation. Second, we find that the ladder operators for the harmonic oscillator generate a $ \mathbb{Z}_2\times\mathbb{Z}_2 $-graded colour Lie superalgebra and we use the operators from this algebra to compute the spectrum. These results illustrate two points: the L\'evy-Leblond equation admits colour Lie superalgebras with gradings higher than $ \mathbb{Z}_2\times\mathbb{Z}_2 $ and colour Lie superalgebras appear for potentials besides the free potential.
Forward citations
Cited by 2 Pith papers
-
On the Classification of the L\'evy-Leblond Spinors
Lévy-Leblond spinors come in real, complex, quaternionic, and chiral types, and the 1+1 conformal case realizes the osp(1|2) superalgebra.
-
On braid statistics versus parastatistics
A report on results that claim to refute the conventionality of parastatistics using 2-bit paraparticles, plus a review of braided Majorana qubits for topological quantum computation.
Discussion (0). Continue with ORCID to comment.