Abstract
We use light-cone gauge formalism to study interacting massive and massless continuous-spin fields and finite component arbitrary spin fields propagating in the flat space. Cubic interaction vertices for such fields are considered. We obtain parity invariant cubic vertices for coupling of one continuous-spin field to two arbitrary spin fields and cubic vertices for coupling of two continuous-spin fields to one arbitrary spin field. Parity invariant cubic vertices for self-interacting massive/massless continuous-spin fields are also obtained. We find the complete list of parity invariant cubic vertices for continuous-spin fields and arbitrary spin fields.
Highlights
Continuous-spin field propagating in flat space is associated with continuous-spin representation of the Poincare algebra
We use light-cone gauge formalism to study interacting massive and massless continuous-spin fields and finite component arbitrary spin fields propagating in the flat space
We find the complete list of parity invariant cubic vertices for continuous-spin fields and arbitrary spin fields
Summary
Continuous-spin field propagating in flat space is associated with continuous-spin representation of the Poincare algebra (for review, see refs. [1]–[3]). [18], we developed the light-cone gauge formulation of massless and massive continuous-spin fields propagating in the flat space Rd−1,1 with arbitrary d ≥ 4.2 in ref. Detailed discussion of light-cone formulation to free continuous-spin fields and arbitrary spin massive/massless fields may be found in section 2 in ref. Discussion of the field theoretical realization of the kinematical and dynamical generators we discuss light-cone gauge description of the continuous-spin field, and arbitrary spin massive and massless fields. In light-cone gauge approach, continuous-spin field, spin-s massive field, and spin-s massless field, are described by the following set of scalar, vector, and tensor fields of the so(d − 2) algebra:. Casimir operators of the Poincare algebra are given by C2 = m2, C4 = κ2, while for arbitrary spin-s massive/massless fields one has the relations C2 = m2, C4 = m2s(s+d−3). The Hamiltonian is obtained from relations (2.16), (2.25)
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