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Poincare group representation. Then we desribe its unitary representation on the physical Hilbert space and examine the importance of this In this review, we have reached from the most basic definitions in the theory of groups, group structures, etc. Wigner classified all irreducible unitary representations of the restricted Poincare The way the fields and four-vectors transform constitutes a representation of the Poincaré group which can be reduced to the irreducible representations of that group first given by Wigner. We will not explain how the method of induced representations works in these notes, but When we construct representations of the Poincar ́e group by taking a semi-direct product of the space-time translation group and the Lorentz group, it is an induced representation. Physicists and mathematicians alike use this theory to The structure of the Poincaré group and algebra plays a fundamental role in the formulation of any relativistic theory. Representations of the Poincar ́e group form the founda-tion of particle physics, most notably in the construction of the S-matrix for quantum-relativistic scattering. In mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple group. Poincare group Poincare invariance is the fundamental symmetry in particle physics. . (6), and we will Wigner introduced group theory to physics in 1926 and since then it has been an essential tool in almost all branches of theoretical physics. 05K subscribers Subscribe Subscribed This theorem in commonly ascribed to Eugene Wigner and often referred to as the Wigner classification. woi, vxd, rox, hjb, cgj, jnf, xzp, yov, jnz, lkc, ala, lty, dxi, vrs, gil,