Title: Conformal invariance and abnormal dimensionalities
Abstract:Conformal invariant field theory in two-dimensional and fourdimensional space-times is considered. It is shown that one has to consider not the conformal group as the group of conformal symmetry, but ...Conformal invariant field theory in two-dimensional and fourdimensional space-times is considered. It is shown that one has to consider not the conformal group as the group of conformal symmetry, but its universal covering that have besides the oneand two-valued representations of the conformal group, also its infinite-valued representations. If one confines oneself to the oneand two-valued representations, the conformal invariance is compatible with axioms of the field theory only in case of the fields with discrete dimensionality d = N/2 + s + n, where N is dimension of the space-time, S is the spin, and n = 0, 1, 2,.... Irreducible representations of the two-dimensional conformal group are considered in detail. The Thirring model is discussed. It is shown that in this model the fields are transformed according to the infinite-dimensional representations of the discrete series. (auth)Read More
Publication Year: 1974
Publication Date: 1974-01-01
Language: en
Type: article
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