Multipole expansion of conserved tensor currents and the number of form factors.

Abstract

We develop a formalism for defining and studying the form factors which describe the coupling of a spin-{ital J} particle through a conserved tensor current to a spin-{ital S} boson. For {ital S}=2, these form factors are the single-graviton gravitational form factors. We investigate the behavior of the various form factors under {ital C}, {ital P}, {ital T}, and {ital CPT} and classify them accordingly. We show that under {ital CPT} invariance all the multipoles of the mass distribution are the same for a particle and its antiparticle. We also show that in a quantum theory of gravity the coupling of a particle to the graviton is in general different from that of its antiparticle. Only when {ital P} and {ital T} are both valid symmetries of the underlying theory do a particle and its antiparticle couple identically to the graviton. The number of form factors for arbitrary {ital J} and {ital S} is given. We show that a massive Majorana particle (a {ital CPT} self-conjugate particle) coupling to an odd-spin boson possesses only anapole moments. Massless Majorana particles with spin{ne}1/2 have no single-photon electromagnetic form factors while the ones with spin{ne}1/2, 1, or 3/2 have no interactions with amore » spin-3 boson; this applies to the graviton ({ital J}=2, {ital S}=1,3) and to the massless gravitino ({ital J}=3/2, {ital S}=1). Our results also apply to extended objects (nuclei, . . .) in the low-energy limit.« less