Completing Multiparticle Representations of the Poincaré Group

Area of Science:

• Theoretical Particle Physics
• Quantum Field Theory
• Scattering Theory

Background:

• Standard S-matrix theory defines asymptotic multiparticle states as tensor products of single-particle states.
• Existing formalisms face challenges in fully describing complex scattering scenarios involving multiple interacting particles.

Purpose of the Study:

• To extend the definition of asymptotic multiparticle states in S-matrix theory.
• To introduce and define novel quantum numbers, termed pairwise helicities, for asymptotically separated particle pairs.
• To generalize existing constructions to accommodate these new states and their associated quantum numbers.

Main Methods:

• Generalized the Wigner construction to independently treat single particles and particle pairs.
• Introduced pairwise helicities (q_ij) as new quantum numbers characterizing particle pair interactions.
• Projected generalized states onto physical states, analyzing their behavior under specific conditions (vanishing q_ij, vanishing spins).

Main Results:

• Developed a new framework for asymptotic multiparticle states that goes beyond simple tensor products.
• Demonstrated that the new states reduce to standard tensor product states when pairwise helicities vanish.
• Showed that vanishing spins reproduce Zwanziger's scalar dyon states, validating the construction.
• Identified pairwise helicity as q_ij = e_i*g_j - e_j*g_i for scattering of electric and magnetic charges.

Conclusions:

• The proposed extension provides a more comprehensive description of asymptotic multiparticle states.
• Pairwise helicities offer a new perspective on the quantum numbers governing particle interactions in scattering.
• The construction successfully describes the asymptotic states for scattering involving electric and magnetic charges.