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What does the Weinberg–Witten theorem want to express?

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The Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton ($j = 2$) cannot be a composite particle in a relativistic quantum field theory. While the argument is so strong and weird, how is it possible? Why can we not construct a theory which is massless charged vector field and therefore carry a Lorentz-covariant current ? And although we assume the second argument is right, which says massless particles with spin $j > 1$ cannot carry a Lorentz-covariant stress-energy, how does it imply that the graviton ($j = 2$) cannot be a composite particle ?

asked Dec 18, 2014 in Theoretical Physics by Alienware (185 points) [ revision history ]
edited Mar 3, 2015 by Arnold Neumaier

Does this SE post answer you question? @Dilaton, have we imported this one?

commented Dec 18, 2014 by Jia Yiyang (2,640 points) [ no revision ]

@JiaYiyang I have just it imported and it is now here.

commented Dec 18, 2014 by Dilaton (6,240 points) [ no revision ]

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