Not sure if this is the right place to ask, but this doubt originated when reading on string theory and so here it goes...(adsbygoogle = window.adsbygoogle || []).push({});

The general canonical energy-momentum tensor (as derived from translation invariance), [tex]T^{\mu\nu}_{C}[/tex] is not symmetric. Also, the general angular momentum conserved current (as derived from lorentz invariance) consists of two parts to it - the orbital angular momentum component and the spin angular momentum component...

[tex]j^{\mu\nu\rho} = T^{\mu\nu}_{C} x^\rho - T^{\mu\rho}_{C} x^\nu + S^{\mu\nu\rho}[/tex]

But, by taking clues from the above angular momentum expression, we can append a suitable term to the generally non-symmetric canonical energy-momentum tensor and modify it (without breaking its conservation) into a symmetric Belinfante tensor...

[tex]T^{\mu\nu}_{C} \to T^{\mu\nu}_{B} [/tex]

Further, the angular momentum tensor can also be modified to absorb the spin term in its orbital momentum term by rewriting it as...

[tex]j^{\mu\nu\rho} = T^{\mu\nu}_{B} x^\rho - T^{\mu\rho}_{B} x^\nu[/tex]

Now, there is no spin operator at all now - at least not explicitly. And we haven't really modified the physics at all. What is then the spin of the system now?

In light cone gauge of bosonic strings, the above (original) spin operator is used to calculate the spins of the massless fields (photon, graviton)...

So, what would the above disappearance of the spin operator mean then? If you say that its not done away with but is just hidden in the last expression above, what rule do we follow in separating the orbital and spin components of angular momentum?

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# Poincare conserved currents : Energy-momentum and Angular-momentum tensors

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