Conformal properties of soft operators. II: Use of null-states. (Conformal properties of soft-operators. II: Use of null-states.) (English) Zbl 1435.83009
Summary: For Part I see [the authors et al., “Conformal properties of soft operators. I: Use of null states”, Phys. Rev. D 101, No. 10, Article ID 106014, 24 p. (2020; doi:10.1103/PhysRevD.101.106014)]. Representations of the (Lorentz) conformal group with the soft operators as highest weight vectors have two universal properties, which we clearly state in this paper. Given a soft operator with a certain dimension and spin, the first property is about the existence of “(large) gauge transformation” that acts on the soft operator. The second property is the decoupling of (large) gauge-invariant null-states of the soft operators from the \(S\)-matrix elements. In each case, the decoupling equation has the form of zero field-strength condition with the soft operator as the (gauge) potential. Null-state decoupling effectively reduces the number of polarisation states of the soft particle and is crucial in deriving soft-theorems from the Ward identities of asymptotic symmetries. To the best of our understanding, these properties are not directly related to the Lorentz invariance of the \(S\)-matrix or the existence of asymptotic symmetries. We also verify that the results obtained from the decoupling of null-states are consistent with the leading and subleading soft-theorems with finite energy massive and massless particles in the external legs.
MSC:
| 83A05 | Special relativity |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 20C35 | Applications of group representations to physics and other areas of science |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 22E15 | General properties and structure of real Lie groups |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
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