Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories

Abstract

We complete the set of spin-projector operators for fields up to rank-3 by providing all operators connecting sectors with same spin and parity. In this way we can broaden the search for unitary and non-tachyonic particle propagation in quadratic lagrangian with interfield mixing. We use the properties of projector algebra to reanalyze known theories and shed light towards new healthy ones. We do so with full control over the gauge constraints by working the form of the saturated propagator in an appropriate frame of reference.

Radiatively stable ghost and tachyon freedom in Metric Affine Gravity

“…Accordingly, this points to the existence of a supportive scalar sector of Stueckelberg/Goldstone nature. By using the extended basis of operator completed in [34] we can show, also a non-trivial result, that such extension does not reintroduce any unstable tuning of parameters. In this work we use the mostly minus metric signature.…”

“…The very same issue has also helped the development of its own methodology to efficiently deal with a large parameter space and to lead, in a more direct way, to the nature of the propagating states. We will now briefly review the algorithm used while referring to [34] and references therein for a more detailed exposition. The propagation of particles is determined by the quadratic part of the action S 2 .…”

“…and the trace is over the hidden Lorentz indices [34]. The projector operators trade, therefore, the complexity of the index structure for the more simple set of matrices a {s,p} i,j .…”

“…where Ψ is an arbitrary, momentum-dependent gauge parameter. Again, beware of our concise notations where Lorentz contraction are hidden and symbols in capital Greek letters represents multiple fields [34]. To find the form of D(q), a gauge fixing is necessary which, in this formalism, is achieved by selecting a non-degenerate submatrix ã{s,p} i,j .…”

“…This is the known realization of gravitational diffeomorphism invariance. We now present the results of the spectral analysis obtained by following the procedure outlined in [34]. Beyond the massless pole, two massive ones are sourced by the 2 − sector, m 2 2 − = a 0 g 4 +4g 1 , and the 0 − one, m 2 0 − = a 0 g 4 −2g 1 .…”