theorems:weinberg-witten_theorem
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theorems:weinberg-witten_theorem [2017/05/07 14:24] jakobadmin |
theorems:weinberg-witten_theorem [2018/04/09 11:12] tesmitekle [Concrete] |
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| ====== Weinberg-Witten Theorem ====== | ====== Weinberg-Witten Theorem ====== | ||
| - | <tabbox Why is it interesting?> | ||
| - | <tabbox Layman?> | + | <tabbox Intuitive> |
| - | <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> | + | |
| - | + | ||
| - | <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 | + | 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 Researcher> | + | |
| - | + | ||
| - | <note tip> | + | |
| - | The motto in this section is: //the higher the level of abstraction, the better//. | + | |
| - | </note> | + | |
| - | + | ||
| - | --> Common Question 1# | + | |
| + | * 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 | ||
| + | * 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 Abstract> |
| + | <blockquote> | ||
| - | --> Common Question 2# | + | Frequently occurring scientific expressions will be abbreviated: quantum |
| + | field theory (QFT). local quantum physics (LQP), point-like (pl), string-like | ||
| + | (sl), string-local quantum field theory (SLFT), power-counting bound (pcb), | ||
| + | spontaneous symmetry breaking (SSB), string theory (ST), the Becchi-RouetStora-Tyutin | ||
| + | gauge formalism (BRST). | ||
| - | + | [...] | |
| - | <-- | + | |
| - | + | ||
| - | <tabbox Examples> | + | |
| - | --> Example1# | + | This does not only lead to the sl replacement of the missing pl massless |
| + | potential but it also **defuses a No-Go theorem by Weinberg and Witten** claiming | ||
| + | that massless energy-momentum tensors do not exist for s ≥ 2 [37]. The correct | ||
| + | statement is that pl conserved massless E-M tensors do not exist; they have to | ||
| + | be replaced by sl E-M tensors which are different as densities but lead to the | ||
| + | same global charges (generators of the Poincare group). | ||
| - | + | <cite>https://arxiv.org/pdf/1612.00003.pdf</cite> | |
| - | <-- | + | |
| - | --> Example2:# | + | </blockquote> |
| - | |||
| - | <-- | ||
| | | ||
| - | <tabbox History> | + | <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. | ||
| + | |||
| + | <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> | </tabbox> | ||
theorems/weinberg-witten_theorem.txt · Last modified: 2022/10/13 21:15 by 71.80.173.84
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