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A remark on the algebra of space-components of current densities

  • Communicationes Breves
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Acta Physica Academiae Scientiarum Hungaricae

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References

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  6. Here and in what follows we use the notations of [9], e.g.:\(\left\langle {0\left| {A_\mu \left( 0 \right)_r } \right|AI\left( k \right)_r } \right\rangle = {{ - M^2 _A \varepsilon _\mu } \mathord{\left/ {\vphantom {{ - M^2 _A \varepsilon _\mu } {\left[ {G_A \sqrt {2\left( {2\pi } \right)^3 } } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {G_A \sqrt {2\left( {2\pi } \right)^3 } } \right]}}\)

  7. Besides the more stringent restrictions on intermediate states the advantage of considering sum rules for vertex functions lies in the linearity of the resulting algebraic equations.

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  9. F. Csikor andI. Montvay, Nuclear Physics,B7, 268, 1968. In this work the width of ϱ- and Al-mesons as well as the charge radius of pions are calculated in terms ofF π andG v in good agreement with experiment. Note that, besides eqs. (4), there are also other equations coming from time-component space-component commutators.

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  10. It can be shown that the situation is unchanged in both cases if we saturate ther-sum-rules with an arbitrary (finite) number of (ϱ, Al- and π-like) poles. We also note that in GFA the Jacobi identity considered byF. Buccella, G. Veneziano, R. Gatto andS. Okubo, Phys. Rev.,149, 1268, 1966 holds trivially. Thus, the necessity for additionalq-number Schwinger terms does not emerge. The GFA gives zero also for the r.h.s. of eq. (25) of this work, in coincidence with the possible (ad hoc) modification proposed by these authors.

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  1. Institute for Theoretical Physics, Roland Eötvös University, Budapest

    I. Montvay

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  1. I. Montvay
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Montvay, I. A remark on the algebra of space-components of current densities. Acta Physica 25, 407–410 (1968). https://doi.org/10.1007/BF03157164

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