Abstract
We propose a unified BRST formulation of general massless fermionic fields of arbitrary mixed-symmetry type in d-dimensional Minkowski space. Depending on the value of the real parameter the system describes either helicity fields or continuous spin fields. Starting with the unified formulation we derive a number of equivalent descriptions including the triplet formulation, Fang-Fronsdal-Labastida formulation, light-cone formulation and discuss the unfolded formulation.
Highlights
A continuous spin parameter denoted by a real number μ is an eigenvalue of the squared iso(d − 2) momentum or of the quartic iso(d − 1, 1) Casimir operator [5]
We propose a unified BRST formulation of general massless fermionic fields of arbitrary mixed-symmetry type in d-dimensional Minkowski space
The standard mass parameter associated to the quadratic iso(d − 1, 1) Casimir operator is zero, m = 0, so that the continuous spin fields are massless fields simultaneously characterized by the dimensionful parameter μ
Summary
Let us introduce Grassmann even variables aaI and aJb , where a, b = 0, . Where ηab = (− + · · · +) is the Minkowski tensor. These variables generate the associative algebra which is promoted to the operator algebra of a quantum constrained system. Consider the linear space Pnd(aI ) = S ⊗ C[aI ], where S is the Dirac representation of the Clifford algebra generated by θa and C[aI ] is the space of polynomials in aaI. The associative algebra generated by aaI , aJb and θa can be represented on Pnd(aI ) in a natural way if one defines the action of the generators according to aaI ψ(a) := aaI ψ(a) , aIaψ(a).
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