advanced_notions:duality
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advanced_notions:duality [2018/04/30 13:27] jakobadmin [Why is it interesting?] |
advanced_notions:duality [2020/04/12 15:04] (current) jakobadmin |
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| <tabbox Concrete> | <tabbox Concrete> | ||
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| This situation is what people call a duality: | This situation is what people call a duality: | ||
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| Jordan-Wigner, bosonization, Wegner, particle-vortex, perhaps others). This word is dangerous (it is one of the forbidden words on my blackboard) because it is about ambiguities | Jordan-Wigner, bosonization, Wegner, particle-vortex, perhaps others). This word is dangerous (it is one of the forbidden words on my blackboard) because it is about ambiguities | ||
| in our (physics) language. <cite>[[https://mcgreevy.physics.ucsd.edu/s14/239a-lectures.pdf|Where do quantum field theories come from?]] by McGreevy</cite></blockquote> | in our (physics) language. <cite>[[https://mcgreevy.physics.ucsd.edu/s14/239a-lectures.pdf|Where do quantum field theories come from?]] by McGreevy</cite></blockquote> | ||
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| + | <blockquote> | ||
| + | There are many theories, which have more than one Lagrangian. So that's the opposite. Either we have no Lagrangian at all or we have more than one Lagrangian. | ||
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| + | <cite>Duality and emergent gauge symmetry - Nathan Seiberg</cite> | ||
| + | </blockquote> | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
| <blockquote> | <blockquote> | ||
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| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| - | Oftentimes in physics, we can only calculate things in terms of a [[advanced_notions:quantum_field_theory:perturbation_theory|perturbation series]]. Especially, in quantum field theory, this is almost always the case. The perturbation series in [[theories:quantum_field_theory|quantum field theory]] is usually a series in the small coupling constant of the interaction in question. However, when this interaction constant becomes too large, such a perturbative approach no longer yields a good approximation. This is especially problematic for quantum chromodynamics at low energies, where the strong coupling constant becomes too large. | + | Oftentimes in physics, we can only calculate things in terms of a [[advanced_notions:quantum_field_theory:perturbation_theory|perturbation series]]. Especially, in quantum field theory, this is almost always the case. The perturbation series in [[theories:quantum_field_theory:canonical|quantum field theory]] is usually a series in the small coupling constant of the interaction in question. However, when this interaction constant becomes too large, such a perturbative approach no longer yields a good approximation. This is especially problematic for quantum chromodynamics at low energies, where the strong coupling constant becomes too large. |
| A duality can be an enormously powerful tool in such a situation. A dual theory describes the same physics, but in a different way. Especially the coupling constant of a dual theory is inversely proportional to the original coupling constant. Hence, whenever the coupling constant becomes too large the calculation can be done in the dual theory instead, where we can work with a small coupling constant. | A duality can be an enormously powerful tool in such a situation. A dual theory describes the same physics, but in a different way. Especially the coupling constant of a dual theory is inversely proportional to the original coupling constant. Hence, whenever the coupling constant becomes too large the calculation can be done in the dual theory instead, where we can work with a small coupling constant. | ||
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| influential development was the discovery of a duality between anti-de Sitter grav- | influential development was the discovery of a duality between anti-de Sitter grav- | ||
| ity and a conformal field theory, sometimes named after its inventor as Maldacena | ity and a conformal field theory, sometimes named after its inventor as Maldacena | ||
| - | conjecture. <cite>Symmetries in Fundamental Physics by Sundermeyer</blockquote> | + | conjecture. <cite>Symmetries in Fundamental Physics by Sundermeyer</cite></blockquote> |
| </tabbox> | </tabbox> | ||
advanced_notions/duality.1525087623.txt.gz · Last modified: 2018/04/30 11:27 (external edit)
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