Prog. Theor. Phys. Supplement No.37 & 38 (1966) pp. 74-93
Current Algebras in a Simple Model
Laboratory for Nuclear Science and Physics Department, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.
(Received June 27, 1966)
We use third and fourth order perturbation theory in a renormalizable interacting quark model to compare operator parts of equal time commutators with their conventionally expected values. In the case of matrix elements between spin-less states, all commutators have extra terms except the V0, A0 algebra, [Vj, Ak], [S, S], [S, P] and [P, P]. If we consider also a neutral vector field coupled to quark number, then [V0, A0] and [Vj, Ak] acquire extra terms. If, in addition, V currents which are even and A currents which are odd under charge conjugation are present, we conjecture that only the doubly integrated V0, A0 algebra remains intact. The same comment applies to S and P currents with negative C parity.
The Jacobi identity in general fails for successive equal time commutators (this is because an interchange of limits is involved, although it holds (in our model) for the V0, A0 algebra).
DOI : 10.1143/PTPS.37.74
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Citing Article(s) :
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Note on Massless Bosonic States in Two-Dimensional Field Theories
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