Why do we say that irreducible representation of Poincare group represents the one-particle state?

Only because

1. Rep is unitary, so saves positive-definite norm (for possibility density),

2. Casimir operators of the group have eigenvalues ${m}^{2}$ and ${m}^{2}s(s+1)$, so characterizes mass and spin, and

3. It is the representation of the global group of relativistic symmetry,

yes?

Only because

1. Rep is unitary, so saves positive-definite norm (for possibility density),

2. Casimir operators of the group have eigenvalues ${m}^{2}$ and ${m}^{2}s(s+1)$, so characterizes mass and spin, and

3. It is the representation of the global group of relativistic symmetry,

yes?