I do not fully understand the general context which is related to Feynman diagram. I prefer to think it as a magic of physicists. This time analysis is a servant of combinatorics.
I don’t know what it is all about. It reminds me
Feng Luo’s course on Kontsevich’s proof of
Witten conjecture. The left hand side of
Theorem 3 is a correlation function of Matrix model.
This can be written differently by adding external source
term (a linear term of H after
the trace(H^2) in the exponential)
in the Gaussian measure. But I don’t
understand the meaning of this result.
The variable N is funny. It is the size of the matrix.
I suspect that it can be extended to
a continuous variable.
You are right. What I presented is just an elementary application of matrix model. First, people established 2D gravity using discrete surface and matrix model. Also there is topological gravity using intersection theory on moduli space. Witten conjecture established the relation between this two approaches. But matrix model itself is interesting e.g., it relates to Ising model. Physicists usually consider the behavior of a model when N goes to infinity.
十一月 6th, 2007 at 1:22 下午
Theorem 3 is due to J. Harer and D. Zagier: The Euler characteristic of the moduli space of curves. Invent. Math. 85 (1986), no. 3, 457–485
十一月 6th, 2007 at 2:35 下午
Cool. Is this really a magic or is there a clue why this is so?
十一月 6th, 2007 at 5:08 下午
I do not fully understand the general context which is related to Feynman diagram. I prefer to think it as a magic of physicists. This time analysis is a servant of combinatorics.
十一月 9th, 2007 at 12:26 下午
I don’t know what it is all about. It reminds me
Feng Luo’s course on Kontsevich’s proof of
Witten conjecture. The left hand side of
Theorem 3 is a correlation function of Matrix model.
This can be written differently by adding external source
term (a linear term of H after
the trace(H^2) in the exponential)
in the Gaussian measure. But I don’t
understand the meaning of this result.
The variable N is funny. It is the size of the matrix.
I suspect that it can be extended to
a continuous variable.
十一月 15th, 2007 at 5:44 下午
You are right. What I presented is just an elementary application of matrix model. First, people established 2D gravity using discrete surface and matrix model. Also there is topological gravity using intersection theory on moduli space. Witten conjecture established the relation between this two approaches. But matrix model itself is interesting e.g., it relates to Ising model. Physicists usually consider the behavior of a model when N goes to infinity.