Abstract
We obtain Proca field theory from the quantisation of the mathcal{N} = 2 supersymmetric worldline upon supplementing the graded BRST-algebra with an extra multiplet of oscillators. The linearised theory describes the BV-extended spectrum of Proca theory, together with a Stückelberg field. When coupling the theory to background fields we derive the Proca equations, arising as consistency conditions in the BRST procedure. We also explore non-abelian modifications, complexified vector fields as well as coupling to a dilaton field. We propose a cubic action on the space of BRST-operators which reproduces the known Proca action.
Highlights
BV-spectrum of the Proca theory together with the linearised equations of motion, it does not allow to promote them to background fields in the BRST operator Q as required for a background independent formulation that produces the non-linear equations of motion by nilpotency of Q as in [19,20,21,22]
We propose a cubic action on the space of BRST-operators which reproduces the known Proca action
Either way, analysing the corresponding constraint algebra and the associated BRST charge we obtain in this way a Proca theory in spacetime, whose dynamics is determined by consistency conditions of the BRST quantisation rather than a variation of some Lagrangian
Summary
The algebra of the constraints does not close, even when the Yang-Mills field is on-shell. The BRST charge, obtained by combining the constraints with their BRST ghosts . On V0 the BRST-operator Q(A) given by (2.3) is nilpotent provided κ = 1 and the Yang-Mills equation [Πμ, [Πμ, Πν]] = 0 is satisfied. The latter equation is implied by the vanishing of the [q, H] commutation relation. From the spacetime point of view this has the interpretation that gluons can consistently propagate on a background that satisfies the Yang-Mills equations while this is not the case for generic excitations contained in the complement of V0 in V
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