theorems:weinberg-witten_theorem

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theorems:weinberg-witten_theorem [2018/01/02 14:06] jakobadmin [Why is it interesting?] |
theorems:weinberg-witten_theorem [2022/10/13 21:15] (current) 71.80.173.84 updated the link for the Loebbert essay |
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====== Weinberg-Witten Theorem ====== | ====== Weinberg-Witten Theorem ====== | ||

- | <tabbox Why is it interesting?> | + | <tabbox Intuitive> |

- | <blockquote>"The Weinberg–Witten theorem states that a massless particle of spin strictly greater than one cannot possess an energy-momentum tensor $T_{\mu \nu}$ which is both Lorentz covariant and gauge invariant. Of course, this no-go theorem does not preclude gravitational interactions. In the spin-two case, it implies that there cannot exist any gauge-invariant energy-momentum tensor for the graviton."<cite>https://arxiv.org/abs/1007.0435</cite></blockquote> | + | |

- | <tabbox Layman?> | + | |

- | <note tip> | + | <blockquote>Higher spin particles have to be coupled to conserved currents, and there are no conserved currents of high spin in quantum field theories. The only conserved currents are vector currents associated with internal symmetries, the stress-energy tensor current, the angular momentum tensor current, and the spin-3/2 supercurrent, for a supersymmetric theory. |

- | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | + | |

- | </note> | + | This restriction on the currents constrains the spins to 0,1/2 (which do not need to be coupled to currents), spin 1 (which must be coupled to the vector currents), spin 3/2 (which must be coupled to a supercurrent) and spin 2 (which must be coupled to the stress-energy tensor). <cite>https://physics.stackexchange.com/a/15164/37286</cite></blockquote> |

- | | + | <tabbox Concrete> |

- | <tabbox Student> | + | |

- | A good introduction to the theorem and its meaning can be found in "[[http://onlinelibrary.wiley.com/doi/10.1002/andp.200810305/epdf|The Weinberg-Witten theorem on massless particles: an essay]]" by Florian Loebbert | + | * A good introduction to the theorem and its meaning can be found in "[[https://pure.mpg.de/rest/items/item_33005_2/component/file_33006/content]]" by Florian Loebbert |

+ | * see also [[https://physics.stackexchange.com/a/15164/37286|this great post]] by Ron Maimon | ||

+ | * Another great discussion can be found in Schwartz' QFT book page 153ff. | ||

- | <tabbox Researcher> | + | <tabbox Abstract> |

<blockquote> | <blockquote> | ||

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</blockquote> | </blockquote> | ||

- | --> Common Question 1# | ||

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- | --> Common Question 2# | ||

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- | <-- | ||

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- | <tabbox Examples> | + | <tabbox Why is it interesting?> |

+ | The punchline of the Weinberg-Witten theorem is that there are no interacting theories of massless particles of spin greater than 2. | ||

- | --> Example1# | + | <blockquote>"The Weinberg–Witten theorem states that a massless particle of spin strictly greater than one cannot possess an energy-momentum tensor $T_{\mu \nu}$ which is both Lorentz covariant and gauge invariant. Of course, this no-go theorem does not preclude gravitational interactions. In the spin-two case, it implies that there cannot exist any gauge-invariant energy-momentum tensor for the graviton."<cite>https://arxiv.org/abs/1007.0435</cite></blockquote> |

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- | <-- | + | |

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- | --> Example2:# | + | |

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- | <-- | + | |

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- | <tabbox History> | + | |

</tabbox> | </tabbox> | ||

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