Massive gravity from descent equations

Abstract

Both massless and massive gravity are derived from descent equations (Wess-Zumino consistency conditions). The massive theory is a continuous deformation of the massless one. *

Regularization in quantum field theory from the causal point of view

“…5.7). The gauge principle even works in massive gravity [38]. The cohomological nature of gauge invariance was analyzed in [39].…”

Perturbative gravity in the causal approach

“…It follows that if we modify conveniently the expressions B µνρσ and B µνρ we make a 1 → a 1 + 2 c, a 2 → a 2 + c with c arbitrary. In particular we can arrange such that a 1 = a 2 ≡ 2 κ (this is the choice made in [14]). In this case one can prove rather easily that T µνρ…”

“…We take I = I 1 ∪ I 2 ∪ I 3 a set of indices and for any index we take a quadruple (v µ a , u a ,ũ a , Φ a ), a ∈ I of fields with the following conventions: (a) the first entry are vector fields and the last three ones are scalar fields; (b) the fields v µ a , Φ a are obeying Bose statistics and the fields u a ,ũ a are obeying Fermi statistics; (c) For a ∈ I 1 we impose Φ a = 0 and we take the masses to be null m a = 0; (d) For a ∈ I 2 we take the all the masses strictly positive: m a > 0; (e) For a ∈ I 3 we take v µ a , u a ,ũ a to be null and the fields Φ a ≡ φ H a of mass m H a ≥ 0; The fields u a ,ũ a , a ∈ I 1 ∪ I 2 and Φ a a ∈ I 2 are called ghost fields and the fields φ H a , a ∈ I 3 are called Higgs fields; (f) we include matter fields also i.e some set of Dirac fields with Fermi statistics: Ψ A , A ∈ I 4 ; (g) we consider that the Hilbert space is generated by all these fields applied on the vacuum and define in H the operator Q according to the following formulas for all indices a ∈ I : Here [·, ·] is the graded commutator. In [14] we have determined the most general interaction between these fields in theorem 6.1:…”

From massive gravity to modified general relativity

“…The most elegant way to obtain the theory is by assuming the G. Scharf (B) Institut für Theoretische Physik, Universität Zürich, Winterthurerstr. 190, 8057 Zurich, Switzerland e-mail: scharf@physik.unizh.ch gauge invariance condition for all chronological products in the form of the descent equations [4]. These give the total interaction Lagrangian including ghost couplings and the necessary coupling to a vector-graviton field.…”

“…In the next section, we introduce the asymptotic free quantum fields of the theory and the gauge structure. Using the lowest order coupling derived previously by gauge invariance [3,4] we discuss the limit of vanishing graviton mass and then the classical limit. The surviving coupling term between the tensor-and vector-graviton field leads to modified general relativity.…”