Lagrangian cohomological couplings among vector fields and matter fields

Abstract

Consistent couplings between a set of vector fields and a system of matter fields are analysed in the framework of Lagrangian BRST cohomology.

Wald type analysis for spin-one fields in three dimensions

“…Thus the identity (19) and the linearized eom F a(1) µ (Ȧ) = 0 implies ∂ a F a(2) µ (Ȧ a ) = 0. In this way, order by order, all the additional equations, are automatically satisfied, by demanding the identity (19) as well as the eom at that order.…”

“…Following Wald, we further assume that the derivative expansion in (19) truncates at first order, and also that the coefficients λ µ aν contains no more than one derivative of A µ a while ρ bµ aν contains no derivatives of A µ a . As mentioned in [5], this is one of the strongest assumption of the entire analysis.…”

Construction of consistent interactions in higher derivative Yang-Mills gauge theory with matter fields

“…Also to get a bigger conceptual picture, a collection of antifields φ * A = (A * µ a , B * µ a , φ * i , Z * i , η * a ) with opposite statistics compared to their partners are needed for the Koszul-Tate resolution of the equations of motion. Then it is customary to introduce the Grassmann parities, antighost, pureghost and ghost numbers both for the fields and antifields as follows [18,35]…”

“…In principle, such BRST deformation procedure can be employed to higher-order deformations where obstructions will arise naturally and the number of the gauge symmetries is kept after the deformations. In the pure gauge theory, it is possible to add gauge invariant terms to the Lagrangian without changing the gauge symmetries [31][32][33], while coupled to matter fields, the required consistent deformations can be deduced from the conservation of the currents resulting from the global invariance of the original gauge-matter system [34,35]. Besides, the deformation procedure will alter the form of the gauge transformations of the matter fields and the deformation parameter can be regarded as the couplings constant among fields.…”

Massive spin-one fields from couplings with five massless real scalars

“…at hand, from the deformed solution to the master equation (12) one can identify the entire gauge structure of the resulting interacting theory. The procedure previously exposed was successfully employed in constructing some gravity-related interacting models [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and also in deducing the consistent couplings in theories that involve various kinds of forms [43][44][45] or matter fields in the presence of gauge forms [46][47][48]. It is worth noticing that a BRST Hamiltonian counterpart to the antifield deformation method was conceived [49].…”