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 inter-field 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.

Ancillary file provided with the new mixing operators connecting different spin/parity sectors. v2: added references and cosmetic-induced changes. Content unchanged. v3: matches published PRD version. Mixing operators are now added in the appendix. Some verbose comments removed, original content stressed, results unchanged

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• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Stability of non-degenerate Ricci-type Palatini theories
• Einstein-Proca theory from the Einstein-Cartan formulation
• Some simple theories of gravity with propagating torsion
• Massive Higher-Spin Multiplets and Asymptotic Freedom in Quantum Gravity