Some criteria are established to test whether invariance under a continuous transformation will lead to a conservation law. The scale transformation is examined as a special case, and shown not only to lead to no general conservation law, but aiso in fact to be of a trivial nature. This is due to the rather artificial way in which scale invariance is usually introduced. A theory is then constructed by introducing an internal coordinate of dimension (length) in order to allow only the dimensionless ratio of lengths to enter; and by exploiting the gauge-like structure of the scale transformation. In this …
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California. Univ., Berkeley. Lawrence Radiation Lab.
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Some criteria are established to test whether invariance under a continuous transformation will lead to a conservation law. The scale transformation is examined as a special case, and shown not only to lead to no general conservation law, but aiso in fact to be of a trivial nature. This is due to the rather artificial way in which scale invariance is usually introduced. A theory is then constructed by introducing an internal coordinate of dimension (length) in order to allow only the dimensionless ratio of lengths to enter; and by exploiting the gauge-like structure of the scale transformation. In this theory the scale transformation does iead to a new conserved current (as well as to an almost conserved'' one), and the internal coordinate is shown to play the same role for the scale transformation as the internal coordinate spin plays for the case of rotations. (auth)
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