Modular invariance in math and physics - 편집 역사

2021년 2월 17일 (수) 09:41에 Pythagoras0님의 편집

2021-02-17T09:41:49Z

2020-12-28T12:14:57Z

2020-12-28T07:33:59Z

메타데이터: 새 문단

2020-11-16T15:51:30Z

2020-11-16T14:47:02Z

2020-11-13T13:55:28Z

2015-03-09T00:27:02Z

2014-05-13T02:29:55Z

2013-09-03T22:47:48Z

2013-07-14T18:13:29Z

@@ 52번째 줄: / 52번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q60367 Q60367]

@@ 6번째 줄: / 6번째 줄: @@
 * Modular invariance in lattice statistical mechanics http://aflb.ensmp.fr/AFLB-26j/aflb26jp287.pdf
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 ==path integral in string theory==
@@ 17번째 줄: / 17번째 줄: @@
 ** compare with http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger_proper_time_formalism
-−
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 ==circle method==
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 ==related items==

← 이전 판		2020년 12월 28일 (월) 07:33 판
51번째 줄:		51번째 줄:
	[[분류:Number theory and physics]]		[[분류:Number theory and physics]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q60367 Q60367]

@@ 49번째 줄: / 49번째 줄: @@
 * Lepowsky, J. "Lie algebras and combinatorics." Proc. Internat. Congr. Math.(Helsinki, 1978)(to appear) (1978). http://www.mathunion.org/ICM/ICM1978.2/Main/icm1978.2.0579.0584.ocr.pdf
 [[분류:개인노트]]
 [[분류:Number theory and physics]]
 [[분류:migrate]]

@@ 12번째 줄: / 12번째 줄: @@
 ==path integral in string theory==
-* [[path integral and moduli space of Riemann surfaces]] :<math>Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\sum_{g=0}^{\infty} g_{s}^{2g-2}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdots</math><br>
+* [[path integral and moduli space of Riemann surfaces]] :<math>Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\sum_{g=0}^{\infty} g_{s}^{2g-2}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdots</math>
 * <math>Z_{1}</math> is an integral over <math>M_1 = \mathbb{H}/SL(2,\mathbb{Z})</math> i.e. the fundamental domain.
-*  string theory (symmetries, modular group) has a natural covariant UV cutoff!<br>
+*  string theory (symmetries, modular group) has a natural covariant UV cutoff!
 ** compare with http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger_proper_time_formalism

@@ 45번째 줄: / 45번째 줄: @@
 ==expositions==
 * Nikolov, Nikolay M., and Ivan T. Todorov. 2004. “Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory”. ArXiv e-print math-ph/0412039. http://arxiv.org/abs/math-ph/0412039.
 * Lepowsky, J. “Affine Lie Algebras and Combinatorial Identities.” In Lie Algebras and Related Topics, edited by David Winter, 130–56. Lecture Notes in Mathematics 933. Springer Berlin Heidelberg, 1982. http://link.springer.com/chapter/10.1007/BFb0093358.
 * Lepowsky, J. "Lie algebras and combinatorics." Proc. Internat. Congr. Math.(Helsinki, 1978)(to appear) (1978). http://www.mathunion.org/ICM/ICM1978.2/Main/icm1978.2.0579.0584.ocr.pdf

@@ 37번째 줄: / 37번째 줄: @@
 * [[Blackhole theory]]
 * [[Hardy-Ramanujan tauberian theorem]]
 ==questions==
@@ 44번째 줄: / 45번째 줄: @@
 ==expositions==
 * Nikolov, Nikolay M., and Ivan T. Todorov. 2004. “Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory”. ArXiv e-print math-ph/0412039. http://arxiv.org/abs/math-ph/0412039.
+* Lepowsky, J. “Affine Lie Algebras and Combinatorial Identities.” In Lie Algebras and Related Topics, edited by David Winter, 130–56. Lecture Notes in Mathematics 933. Springer Berlin Heidelberg, 1982. http://link.springer.com/chapter/10.1007/BFb0093358.
 [[분류:개인노트]]
 [[Category:research topics]]
 [[분류:Number theory and physics]]

← 이전 판		2013년 9월 3일 (화) 22:47 판
37번째 줄:		37번째 줄:
	* [[Blackhole theory]]		* [[Blackhole theory]]
	* [[Hardy-Ramanujan tauberian theorem]]		* [[Hardy-Ramanujan tauberian theorem]]
		+
		+	==questions==
		+	* http://mathoverflow.net/questions/115225/the-dedekind-eta-function-in-physics