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theorems:weinberg-witten_theorem [2018/01/02 14:08]
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
-The punchline of the Weinberg-Witten theorem is that there are no interacting theories of massless particles of spin greater than 2.+
  
-<​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 caseit implies that there cannot exist any gauge-invariant energy-momentum tensor ​for the graviton."<​cite>​https://​arxiv.org/​abs/​1007.0435</​cite></​blockquote>​ +<​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.
-<tabbox Layman?> ​+
  
-<note tip> +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 supercurrent) and spin 2 (which must be coupled to the stress-energy tensor)<​cite>​https://​physics.stackexchange.com/​a/​15164/​37286</cite></​blockquote
-Explanations in this section should contain no formulasbut instead colloquial things like you would hear them during ​coffee break or at a cocktail party. +<​tabbox ​Concrete
-</note> +
-  ​ +
-<​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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-<​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>​
  
  
theorems/weinberg-witten_theorem.1514898496.txt.gz · Last modified: 2018/01/02 13:08 (external edit)