Gravity from Poincare Gauge Theory of the Fundamental Particles. IV: Mass and Energy of Particle Spectrum

Abstract

Particle spectrum of Poincaré gauge theory is investigated in detail, in particular paticle's mass and energy. Besides usual graviton, the torsion field gives rise to massive 2+, 2-, 1+, 1-, 0+ and 0- particles, each of which obeys the Klein-Gordon equation. We find that there are at most three normal particles, defined by having positive mass and positive energy; namely, only nine possible triplets, (2+, 1+, 0-), (2+, 1-, 0-), (2+, 0+, 0-) and their parity conjugate, and (1+, 0+, 0-) and its parity conjugate and finally (1+, 1-, 0-). Further reduction to two and one particles is also possible provided 2+ and 2- cannot coexist. Conditions of nine parameters, α, β, γ, a1, a2, …, a6, for these normal particles to exist are also obtained.