1.1: Poincare Algebra defined

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Jun 3, 2019
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- 1.0: Prelude to Poincare Algebra
- 1.2: Comments on the Poincare Algebra

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In order to desc¡ibe a physical system which is Lorentz invaria¡t one must construct from the fundamental dynamical va¡iables for the system ten Hermitian operators: $H$ , $P^{j}$ , $J^i$ , K^j}\) where (where $j = 1,2,3$ ) satisfying

$P^j, P^k]=0$

$P^j, H]=0$

$[J^j,P^k] = i \hbar \epsilon_{ijk}P^l$

$J^j, H]=0$

$[J^j,J^k] = i \hbar \epsilon_{ijk}J^l$

where $\hbar = h/2\pi$ , $h$ is Planck's constant, $c$ is the speed of light, $\delta_{ij}$ is the Kronecker delta symbol and $\epsilon_ijl$ is the Levi-Civita permutation symbol.

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