A Note on the scale symmetry and Noether current

1998/07/13 by Naohisa Ogawa, Ogawa, Naohisa
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9807086

6pages, No figures, Latex, References are added

arxiv created 1998/09/08 · arxiv updated 2009/11/30

Abstract

Usually we consider the symmetry of action as the symmetry of the theory, however, in the Keplar problem the scaling symmetry existing in equa tion of motion is not the ones for action. It changes the multiplicative c onstant of action and the time boundary. In such a case that the scale tran sformation does not leave the action invariant but keeping the equation inva riant, the following statement is proved. The time integration of Lagrangian is explicitly performed and the action ca n be expressed by the difference of formal (non-conserved) Noether charges a t time boundaries. In field theory the action can be expressed by the bound ary integration of the formal Noether current.

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