Bethe ansatz for RSOS models - 편집 역사

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imported>Pythagoras0: 새 문서: ==related items== * Bethe ansatz * RSOS models * Level restricted Q-system and RSOS model ==articles== * Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz...

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새 문서: ==related items== * Bethe ansatz * RSOS models * Level restricted Q-system and RSOS model ==articles== * Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz...

새 문서

==related items==
* [[Bethe ansatz]]
* [[RSOS models]]
* [[Level restricted Q-system and RSOS model]]

==articles==
* Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz system with q a root of unity. Nuclear Physics B, 389(1), 209–244. doi:[http://dx.doi.org/10.1016/0550-3213(93)90291-V 10.1016/0550-3213(93)90291-V]
* Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:[http://dx.doi.org/10.1088/0305-4470/23/9/012 10.1088/0305-4470/23/9/012].
* Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:[http://dx.doi.org/10.1142/S0217751X89000042 10.1142/S0217751X89000042].

@@ 5번째 줄: / 5번째 줄: @@
 ==TBA equation==
 * taken from [[T-systems and Y-systems in integrable systems]]
-* RSOS model associated with the representation $W_{s}^{(p)}$ of $U_q(\hat{\mathfrak{g}})$.
+* RSOS model associated with the representation <math>W_{s}^{(p)}</math> of <math>U_q(\hat{\mathfrak{g}})</math>.
-* $N$ : length of sites
+* <math>N</math> : length of sites
-* $C=(C_{ab})$ : Cartan matrix
+* <math>C=(C_{ab})</math> : Cartan matrix
-* $L=\ell +h^{\vee}$
+* <math>L=\ell +h^{\vee}</math>
 The Bethe equation is the following
 for the unknowns
-$\{u^{(a)}_j \vert \, a \in I, 1 \le j \le n_a \}$:
+<math>\{u^{(a)}_j \vert \, a \in I, 1 \le j \le n_a \}</math>:
 \begin{equation}\label{ber}
@@ 25번째 줄: / 25번째 줄: @@
 u^{(a)}_j - u^{(b)}_k + \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)}.
 \end{equation}
-Here $n_a=Ns(C^{-1})_{a p}$ as in (3.51)
+Here <math>n_a=Ns(C^{-1})_{a p}</math> as in (3.51)
-with $(r_i,s_i)=(p,s)$ for all $i$, and
+with <math>(r_i,s_i)=(p,s)</math> for all <math>i</math>, and
-$\Omega_a$ is a root of unity
+<math>\Omega_a</math> is a root of unity

← 이전 판		2020년 11월 13일 (금) 15:31 판
45번째 줄:		45번째 줄:
	* Reshetikhin, N.Yu., and P.B. Weigmann. 1987. “Towards the Classification of Completely Integrable Quantum Field Theories (the Bethe-Ansatz Associated with Dynkin Diagrams and Their Automorphisms).” Physics Letters B 189 (1–2) (April 30): 125–131. doi:[http://dx.doi.org/10.1016/0370-2693(87)91282-2 10.1016/0370-2693(87)91282-2].		* Reshetikhin, N.Yu., and P.B. Weigmann. 1987. “Towards the Classification of Completely Integrable Quantum Field Theories (the Bethe-Ansatz Associated with Dynkin Diagrams and Their Automorphisms).” Physics Letters B 189 (1–2) (April 30): 125–131. doi:[http://dx.doi.org/10.1016/0370-2693(87)91282-2 10.1016/0370-2693(87)91282-2].
	* Reshetikhin, N. Yu. 1987. “The Spectrum of the Transfer Matrices Connected with Kac-Moody Algebras.” Letters in Mathematical Physics 14 (3) (October 1): 235–246. doi:10.1007/BF00416853.		* Reshetikhin, N. Yu. 1987. “The Spectrum of the Transfer Matrices Connected with Kac-Moody Algebras.” Letters in Mathematical Physics 14 (3) (October 1): 235–246. doi:10.1007/BF00416853.
		+	[[분류:migrate]]

@@ 38번째 줄: / 38번째 줄: @@
 ==articles==
-* http://dx.doi.org/10.1016/j.nuclphysb.2004.07.008
+* Babichenko, A. 2004. “From S-matrices to the Thermodynamic Bethe Ansatz.” Nuclear Physics B 697 (3) (October 11): 481–512. doi:[http://dx.doi.org/10.1016/j.nuclphysb.2004.07.008 10.1016/j.nuclphysb.2004.07.008].
 * Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz system with q a root of unity. Nuclear Physics B, 389(1), 209–244. doi:[http://dx.doi.org/10.1016/0550-3213(93)90291-V 10.1016/0550-3213(93)90291-V]
 * Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:[http://dx.doi.org/10.1088/0305-4470/23/9/012 10.1088/0305-4470/23/9/012].
 * Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:[http://dx.doi.org/10.1142/S0217751X89000042 10.1142/S0217751X89000042].
-* http://dx.doi.org/10.1016/0370-2693(87)91282-2
+* Reshetikhin, N.Yu., and P.B. Weigmann. 1987. “Towards the Classification of Completely Integrable Quantum Field Theories (the Bethe-Ansatz Associated with Dynkin Diagrams and Their Automorphisms).” Physics Letters B 189 (1–2) (April 30): 125–131. doi:[http://dx.doi.org/10.1016/0370-2693(87)91282-2 10.1016/0370-2693(87)91282-2].
 * Reshetikhin, N. Yu. 1987. “The Spectrum of the Transfer Matrices Connected with Kac-Moody Algebras.” Letters in Mathematical Physics 14 (3) (October 1): 235–246. doi:10.1007/BF00416853.

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-* chapter 15 of [[T-systems and Y-systems in integrable systems]]
+* see chapter 15 of [[T-systems and Y-systems in integrable systems]] for basics
@@ 38번째 줄: / 38번째 줄: @@
 ==articles==
 * Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz system with q a root of unity. Nuclear Physics B, 389(1), 209–244. doi:[http://dx.doi.org/10.1016/0550-3213(93)90291-V 10.1016/0550-3213(93)90291-V]
 * Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:[http://dx.doi.org/10.1088/0305-4470/23/9/012 10.1088/0305-4470/23/9/012].
 * Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:[http://dx.doi.org/10.1142/S0217751X89000042 10.1142/S0217751X89000042].
 * Reshetikhin, N. Yu. 1987. “The Spectrum of the Transfer Matrices Connected with Kac-Moody Algebras.” Letters in Mathematical Physics 14 (3) (October 1): 235–246. doi:10.1007/BF00416853.

@@ 8번째 줄: / 8번째 줄: @@
 * $N$ : length of sites
 * $C=(C_{ab})$ : Cartan matrix
 The Bethe equation is the following

@@ 34번째 줄: / 34번째 줄: @@
 * [[RSOS models]]
 * [[Level restricted Q-system and RSOS model]]
+* [[Fermionic formula for fusion ring]]

← 이전 판		2013년 6월 28일 (금) 15:48 판
1번째 줄:		1번째 줄:
		+	==introduction==
		+	* chapter 15 of [[T-systems and Y-systems in integrable systems]]
		+
		+
		+	==TBA equation==
		+	* taken from [[T-systems and Y-systems in integrable systems]]
		+	* RSOS model associated with the representation $W_{s}^{(p)}$ of $U_q(\hat{\mathfrak{g}})$.
		+	* $N$ : length of sites
		+	* $C=(C_{ab})$ : Cartan matrix
		+
		+	The Bethe equation is the following
		+	for the unknowns
		+	$\{u^{(a)}_j \vert \, a \in I, 1 \le j \le n_a \}$:
		+
		+	\begin{equation}\label{ber}
		+	\Biggl(\frac{\sinh{\pi\over 2L}\bigl(
		+	u^{(a)}_j - \sqrt{-1}{s \over t_p}\delta_{a p}\bigr)}
		+	{\sinh{\pi\over 2L}\bigl(
		+	u^{(a)}_j + \sqrt{-1}{s \over t_p}\delta_{a p}\bigr)}
		+	\Biggr)^N = \Omega_a \prod_{b=1}^r\prod_{k=1}^{n_b}
		+	\frac{\sinh{\pi\over 2L}\bigl(
		+	u^{(a)}_j - u^{(b)}_k - \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)}
		+	{\sinh{\pi\over 2L}\bigl(
		+	u^{(a)}_j - u^{(b)}_k + \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)}.
		+	\end{equation}
		+	Here $n_a=Ns(C^{-1})_{a p}$ as in (3.51)
		+	with $(r_i,s_i)=(p,s)$ for all $i$, and
		+	$\Omega_a$ is a root of unity
		+
		+
	==related items==		==related items==
	* [[Bethe ansatz]]		* [[Bethe ansatz]]

← 이전 판		2013년 6월 28일 (금) 15:24 판
10번째 줄:		10번째 줄:
	* Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:[http://dx.doi.org/10.1088/0305-4470/23/9/012 10.1088/0305-4470/23/9/012].		* Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:[http://dx.doi.org/10.1088/0305-4470/23/9/012 10.1088/0305-4470/23/9/012].
	* Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:[http://dx.doi.org/10.1142/S0217751X89000042 10.1142/S0217751X89000042].		* Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:[http://dx.doi.org/10.1142/S0217751X89000042 10.1142/S0217751X89000042].
		+	* Reshetikhin, N. Yu. 1987. “The Spectrum of the Transfer Matrices Connected with Kac-Moody Algebras.” Letters in Mathematical Physics 14 (3) (October 1): 235–246. doi:10.1007/BF00416853.