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Scalum turns out to be a new inner degree of freedom. Yukawa and Yennie [22] [23] once contemplated that there should appear new “inner motion” degree of freedom in a nonlocal system, later it proved to be trivial due to their wrongly interpreting manner.

has been cited by the following article:

• TITLE: Scaling Transformation for Nonlocal Interactions

  AUTHORS: Hai-Jun Wang

  KEYWORDS: Scaling Transformation, Renormalization, Conservation Law, Spin Crisis, Nonlocal Scattering

  JOURNAL NAME: Journal of Modern Physics, Vol.6 No.5, April 28, 2015

  ABSTRACT: In the light of their relationships with renormalization, in this paper we associate the scaling transformation with nonlocal interactions. On one hand, the association leads us to interpret the nonlocality with locally symmetric method. On the other hand, we find that the nonlocal interaction between hadrons could be test ground for scaling transformation if ascribing the running effects in renormalization to scaling transformation. The nonlocal interaction Lagrangian turns out to vary under scaling transformation, analogous to running cases in renormalization. And the total Lagrangian becomes scale invariant only under some extreme conditions. The conservation law of this extreme Lagrangian is discussed and a contribution named scalum appears to the spin angular momentum. Finally a mechanism is designed to test the scaling effect on nonlocal interaction.