"Quantum spectral curve"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
* A quantum curve is a Schrodinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. | * A quantum curve is a Schrodinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. | ||
| + | * One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. | ||
| + | * If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. | ||
| + | * This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions. | ||
| + | * moduli spaces of quantum curves. | ||
| + | * how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve) | ||
* The Schrodinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed in a rather different way via topological recursion. | * The Schrodinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed in a rather different way via topological recursion. | ||
2015년 4월 7일 (화) 23:12 판
introduction
- A quantum curve is a Schrodinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way.
- One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const.
- If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve.
- This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions.
- moduli spaces of quantum curves.
- how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve)
- The Schrodinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed in a rather different way via topological recursion.
articles
- Luu, Martin, and Albert Schwarz. ‘Fourier Duality of Quantum Curves’. arXiv:1504.01582 [hep-Th, Physics:math-Ph], 7 April 2015. http://arxiv.org/abs/1504.01582.
- Norbury, Paul. ‘Quantum Curves and Topological Recursion’. arXiv:1502.04394 [math-Ph], 15 February 2015. http://arxiv.org/abs/1502.04394.
- Gromov, Nikolay, Vladimir Kazakov, Sebastien Leurent, and Dmytro Volin. “Quantum Spectral Curve for Arbitrary State/operator in AdS$_5$/CFT$_4$.” arXiv:1405.4857 [hep-Th, Physics:math-Ph], May 19, 2014. http://arxiv.org/abs/1405.4857.
- Schwarz, Albert. ‘Quantum Curves’. arXiv:1401.1574 [hep-Th, Physics:math-Ph], 7 January 2014. http://arxiv.org/abs/1401.1574.