Z k parafermion theory - 편집 역사

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introduction

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@@ 48번째 줄: / 48번째 줄: @@
 [[분류:개인노트]]
 [[분류:conformal field theory]]
 [[분류:migrate]]

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 * parafermionic Hilbert space
 * defined by the algebra of parafermionic fields <math>\psi_1</math> and <math>\psi _1^{\dagger }</math> of dimension 1-1/k and central charge
-$$c=\frac{k \dim \mathfrak{g}}{k+h^{\vee}}-\operatorname{rank}\mathfrak{g}=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}$$
+:<math>c=\frac{k \dim \mathfrak{g}}{k+h^{\vee}}-\operatorname{rank}\mathfrak{g}=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}</math>
-where $\mathfrak{g}=\mathfrak{sl}_2$ and $k=2$
+where <math>\mathfrak{g}=\mathfrak{sl}_2</math> and <math>k=2</math>
-* the highest-weight modules are parametrized by an integer (Dynkin label) $l$ with <math>0\leq l < k</math>
+* the highest-weight modules are parametrized by an integer (Dynkin label) <math>l</math> with <math>0\leq l < k</math>
 * <math>\mathbb{Z}_k</math> parafermion theory is known to be equivalent to the coset <math>\hat{\text{su}}(2)_k/\hat{u}(1)_k</math>
 * Kac and Peterson (1984) obtained expression for the parafermion characters
@@ 11번째 줄: / 11번째 줄: @@
 ==examples==
-* $k=1$, [[Ising models]]
+* <math>k=1</math>, [[Ising models]]
-* $k=2$, [[3-states Potts model]]
+* <math>k=2</math>, [[3-states Potts model]]
@@ 43번째 줄: / 43번째 줄: @@
 ==articles==
-* Bianchini, Davide, Elisa Ercolessi, Paul A. Pearce, and Francesco Ravanini. ‘RSOS Quantum Chains Associated with Off-Critical Minimal Models and $\mathbb{Z}_n$ Parafermions’. arXiv:1412.4942 [cond-Mat, Physics:hep-Th, Physics:math-Ph], 16 December 2014. http://arxiv.org/abs/1412.4942.
+* Bianchini, Davide, Elisa Ercolessi, Paul A. Pearce, and Francesco Ravanini. ‘RSOS Quantum Chains Associated with Off-Critical Minimal Models and <math>\mathbb{Z}_n</math> Parafermions’. arXiv:1412.4942 [cond-Mat, Physics:hep-Th, Physics:math-Ph], 16 December 2014. http://arxiv.org/abs/1412.4942.
 * Fateev, V. A., and Al. B. Zamolodchikov. “Integrable Perturbations of ZN Parafermion Models and the O(3) Sigma Model.” Physics Letters B 271, no. 1–2 (November 14, 1991): 91–100. doi:10.1016/0370-2693(91)91283-2.
 * Bilal, Adel. “Bosonization of ZN Parafermions and su(2)N KAČ-Moody Algebra.” Physics Letters B 226, no. 3–4 (August 10, 1989): 272–78. doi:[http://dx.doi.org/10.1016/0370-2693%2889%2991194-5 10.1016/0370-2693(89)91194-5].

← 이전 판		2020년 11월 13일 (금) 05:37 판
50번째 줄:		50번째 줄:
	[[분류:thesis]]		[[분류:thesis]]
	[[분류:conformal field theory]]		[[분류:conformal field theory]]
		+	[[분류:migrate]]

@@ 43번째 줄: / 43번째 줄: @@
 ==articles==
 * Fateev, V. A., and Al. B. Zamolodchikov. “Integrable Perturbations of ZN Parafermion Models and the O(3) Sigma Model.” Physics Letters B 271, no. 1–2 (November 14, 1991): 91–100. doi:10.1016/0370-2693(91)91283-2.
 * Bilal, Adel. “Bosonization of ZN Parafermions and su(2)N KAČ-Moody Algebra.” Physics Letters B 226, no. 3–4 (August 10, 1989): 272–78. doi:[http://dx.doi.org/10.1016/0370-2693%2889%2991194-5 10.1016/0370-2693(89)91194-5].

@@ 43번째 줄: / 43번째 줄: @@
 ==articles==
 * Fateev, V. A., and Al. B. Zamolodchikov. “Integrable Perturbations of ZN Parafermion Models and the O(3) Sigma Model.” Physics Letters B 271, no. 1–2 (November 14, 1991): 91–100. doi:10.1016/0370-2693(91)91283-2.
 * Bilal, Adel. “Bosonization of ZN Parafermions and su(2)N KAČ-Moody Algebra.” Physics Letters B 226, no. 3–4 (August 10, 1989): 272–78. doi:[http://dx.doi.org/10.1016/0370-2693%2889%2991194-5 10.1016/0370-2693(89)91194-5].
 [[분류:개인노트]]
 [[분류:thesis]]
 [[분류:conformal field theory]]

@@ 32번째 줄: / 32번째 줄: @@
 * [[Graded parafermion theory]]
 ==expositions==
 * Gepner, [http://www.integrable-qft.uni-wuppertal.de/program/Gepner.pdf Level Two String Functions and Rogers Ramanujan Type Identities]
 * http://physics.stackexchange.com/questions/76617/what-is-parafermion-in-condensed-matter-physics
 ==articles==

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
 * parafermionic Hilbert space
-* defined by the algebra of parafermionic fields <math>\psi_1</math> and <math>\psi _1^{\dagger }</math> of dimension 1-1/k and central charge $$c=\frac{k \dim \mathfrak{g}}{k+h^{\vee}}=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}$$
+* defined by the algebra of parafermionic fields <math>\psi_1</math> and <math>\psi _1^{\dagger }</math> of dimension 1-1/k and central charge
 where $\mathfrak{g}=\mathfrak{sl}_2$ and $k=2$
 * the highest-weight modules are parametrized by an integer (Dynkin label) $l$ with <math>0\leq l < k</math>
@@ 8번째 줄: / 9번째 줄: @@
 * Lepowsky-Primc (1985) expression in fermionic form
 * third expression
 ==examples==

@@ 37번째 줄: / 37번째 줄: @@
 ==articles==
 * Gepner, Doron. “On The Characters of Parafermionic Field Theories.” arXiv:1410.1778 [hep-Th, Physics:math-Ph], October 7, 2014. http://arxiv.org/abs/1410.1778.
 * Belavin, Alexander A., and Doron R. Gepner. “Generalized Rogers Ramanujan Identities Motivated by AGT Correspondence.” Letters in Mathematical Physics 103, no. 12 (December 1, 2013): 1399–1407. doi:10.1007/s11005-013-0653-2.
 * Genish, A., and D. Gepner. “Level Two String Functions and Rogers Ramanujan Type Identities.” arXiv:1405.1387 [hep-Th, Physics:math-Ph], May 6, 2014. http://arxiv.org/abs/1405.1387.
 * Keegan, Sinéad, and Werner Nahm. 2011. “Nahm’s conjecture and coset models.” <em>1103.4986</em> (March 25). http://arxiv.org/abs/1103.4986
 * Fortin, J.-F., P. Mathieu, and S. O. Warnaar. 2006. “Characters of Graded Parafermion Conformal Field Theory”. ArXiv e-print hep-th/0602248. http://arxiv.org/abs/hep-th/0602248.
 * Schilling, Anne, and S. Ole Warnaar. “Conjugate Bailey Pairs.” arXiv:math/9906092, June 14, 1999. http://arxiv.org/abs/math/9906092.
-* Cabra, D. C. 1998. “Spinons and Parafermions in Fermion Cosets.” In Supersymmetry and Quantum Field Theory, edited by Julius Wess and Vladimir P. Akulov, 220–229. Lecture Notes in Physics 509. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0105250.
+* Georgiev, Galin. ‘Combinatorial Constructions of Modules for Infinite-Dimensional Lie Algebras, II. Parafermionic Space’. arXiv:q-alg/9504024, 25 April 1995. http://arxiv.org/abs/q-alg/9504024.
-* Fateev, V. A., and Al. B. Zamolodchikov. “Integrable Perturbations of ZN Parafermion Models and the O(3) Sigma Model.” Physics Letters B 271, no. 1–2 (November 14, 1991): 91–100. doi:10.1016/0370-2693(91)91283-2.
+* Georgiev, Galin. ‘Combinatorial Constructions of Modules for Infinite-Dimensional Lie Algebras, I. Principal Subspace’. arXiv:hep-th/9412054, 6 December 1994. http://arxiv.org/abs/hep-th/9412054.
-* Bilal, Adel. “Bosonization of ZN Parafermions and su(2)N KAČ-Moody Algebra.” Physics Letters B 226, no. 3–4 (August 10, 1989): 272–78. doi:[http://dx.doi.org/10.1016/0370-2693%2889%2991194-5 10.1016/0370-2693(89)91194-5].
+*  B. Feigin and A. Stoyanovsky, Functional models for representations of current algebras and semi-infinite Schubert cells cf. also the short version . Func. Anal. Appl. 28 (1994), p. 15.
-* Gepner, Doron, and Zongan Qiu. 1987. “Modular Invariant Partition Functions for Parafermionic Field Theories.” Nuclear Physics B 285: 423–453. doi:[http://dx.doi.org/10.1016/0550-3213%2887%2990348-8 10.1016/0550-3213(87)90348-8].
+*  B. Feigin and A. Stoyanovsky, Quasi-particles models for the representations of Lie algebras and geometry of flag manifold. preprint RIMS-942 (1993) hep-th/9308079 http://arxiv.org/abs/hep-th/9308079
 * Gepner, Doron. 1987. “New Conformal Field Theories Associated with Lie Algebras and Their Partition Functions.” Nuclear Physics B 290: 10–24. doi:[http://dx.doi.org/10.1016/0550-3213(87)90176-3 10.1016/0550-3213(87)90176-3].
-* Lepowsky, James, and Mirko Primc. 1985. Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$. Vol. 46. Contemporary Mathematics. American Mathematical Society, Providence, RI. http://www.ams.org/mathscinet-getitem?mr=814303.
+* '''[LP1985]''' Lepowsky, James, and Mirko Primc. 1985. Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$. Vol. 46. Contemporary Mathematics. American Mathematical Society, Providence, RI. http://www.ams.org/mathscinet-getitem?mr=814303.
 * Kac, Victor G, and Dale H Peterson. 1984. “Infinite-dimensional Lie Algebras, Theta Functions and Modular Forms.” Advances in Mathematics 53 (2) (August): 125–264. doi:[http://dx.doi.org/10.1016/0001-8708%2884%2990032-X 10.1016/0001-8708(84)90032-X].