Spin Tensor
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High Quality Content by WIKIPEDIA articles! In mathematics and mathematical physics, the Euclidean group SE(d) of direct isometries is generated by translations and rotations. Its Lie algebra is written mathfrak{se}(d). The Noether currents for the translations make up the stress-energy tensor T^{munu} ,. It satisfies the continuity equation partial_nu T^{munu}=0. And int d^dx T^{mu 0}(vec{x},t) gives the energy-momentum P^mu , at time t, which is time-independent. The Noether current for a rotation about the point y is given by M^{alphabetamu}_y. Because of the Lie algebra relations, M^{alpha...
High Quality Content by WIKIPEDIA articles! In mathematics and mathematical physics, the Euclidean group SE(d) of direct isometries is generated by translations and rotations. Its Lie algebra is written mathfrak{se}(d). The Noether currents for the translations make up the stress-energy tensor T^{munu} ,. It satisfies the continuity equation partial_nu T^{munu}=0. And int d^dx T^{mu 0}(vec{x},t) gives the energy-momentum P^mu , at time t, which is time-independent. The Noether current for a rotation about the point y is given by M^{alphabetamu}_y. Because of the Lie algebra relations, M^{alphabetamu}_y(x)=M^{alphabetamu}_0(x)+y^alpha T^{betamu}(x)-y^beta T^{alphamu}(x), where 0 is the origin. And int d^dx M^{munu}_0(vec{x},t) gives the angular momentum M^{munu} , at time t.
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