Riemann Zeta Function and Functional Equation VII

Japanese version
In 3 dimensions Cardy formula for c=1 is identified with Hardy-Ramanujan formula. This relationship is led from 2 dimensional conformal field theory get rise on the singularities of 3d gravity theory.

Riemann Zeta Function and Functional Equation VII (tentative version)

the original Japanese document:

Riemann Zeta Function and Functional Equation VII (in Japanese)

Then I think that Number Theory is not pure Mathematics but Physics of the world of numbers and even if God does not play dices, instead, Prime Numbers play dices and might construct Quantum Gravity Theory.

General Relativity and Black Holes II

Japanese version
It is simply described on the classification by mass, angular momentum and charge, Ciama's formula, and 2+1 dimensional black holes. In 2+1 dimensional it contains the work of Brown and Henneaux, Cardy formula, and BTZ black holes. Why are 2+1 dimensional black holes important? Because they are very much resemble to 3+1 dimensional ones, in our universe.

General Relativity and Black Holes II

This article is translated into English from my Japanese document for explanation of the elementary part of the theory of Black Holes.

the original Japanese document:

General Relativity and Black Holes II (in Japanese)

General Relativity and Black Holes

Japanese version
It is simply described on Einstein equation, the resemblance of Black holes to the classical thermodynamics and Bekenstein- Hawking entropy formula.

General Relativity and Black Holes

This article is translated into English from my Japanese document for explanation of the elementary part of the theory of Black Holes.

the original Japanese document:

General Relativity and Black Holes

Witten on 2+1 Dimensional Gravity II

Japanese version
In 7 May. 2007 Mr. Lubos Motl had posted an article "Monstrous symmetry of black holes: beauty and the beast" on his BLOG. I translated it into Japanese. It is related to the article of Mr. Woit titled "Witten on 2+1 Dimensional Gravity," and of course closely related to the Witten's paper, "Three-Dimensional Gravity Revisited."

The original BLOG is:

Monstrous symmetry of black holes: beauty and the beast (in English)

and its translation is:

Monstrous symmetry of black holes: beauty and the beast (in Japanese)

Witten on 2+1 Dimensional Gravity

Japanese version
In 6 May. 2007 Mr. Peter Woit had posted an article titled "Witten on 2+1 Dimensional Gravity." I translated it into Japanese. Of course Mr. Witten had published "2+1 Dimensional Gravity as an Exactly Solvable System" in 1988, by which he won the Fields prize. But on the paper titled "Three-Dimensional Gravity Revisited" he reconsidered the older paper and proposed a new idea of 3 dimensional gravity theory.

The original blog by P. Woit is

Witten on 2+1 Dimensional Gravity (in English)

My translation into Japanse is

Witten on 2+1 Dimensional Gravity (in Japanese)

The Witten's paper is published on arxiv.

Three-Dimensional Gravity Revisited

The older paper also can be refered on Internet.

2 + 1 DIMENSIONAL GRAVITY AS AN EXACTLY SOLUBLE SYSTEM

Futhermore, the lecture of this subject is published on YouTube.

Edward Witten Lecture - Dimensional Gravity Revisited (1/6)-GzY
Edward Witten Lecture - Dimensional Gravity Revisited (2/6)-GzY
Edward Witten Lecture - Dimensional Gravity Revisited (3/6)-GzY
Edward Witten Lecture - Dimensional Gravity Revisited (4/6)-GzY
Edward Witten Lecture - Dimensional Gravity Revisited (5/6)-GzY
Edward Witten Lecture - Dimensional Gravity Revisited (6/6)-GzY

Monstrous Moonshine and Mirror Symmetry II

Japanese version
"Monstrous Moonshine and Mirror Symmetry II" is the continue of the last post.

Monstrous Moonshine and Mirror Symmetry II(in English)

Monstrous Moonshine and Mirror Symmetry II(in Japanese)

Monstrous Moonshine and Mirror Symmetry I

Japanese version
In about 2002 I was very much impressed by an article titled "Monstrous Moonshine and Mirror Symmetry," which was described in the Home page of Helena Verrill (Now professor of Louisiana UNIV.). Just 1 years ago I posted on my Japanese BLOG with her permission.

Monstrous Moonshine and Mirror Symmetry I(in English)

Monstrous Moonshine and Mirror Symmetry I(in Japanese)

Some Stories by Prof. Lieven le Bruyn on Arithmetic Topology

Japanese version

Move to Here

Some discussions on "Langlands Programme?"

Japanese version
Though very long disscussion, very interesting dicussion had been appeared on n-cafe, titled "What is the Langlands Programme?." I had translated them into Japanese and post on my BLOG.

The original discussion:

What is the Langlands Programme?

and their translation:

What is the Langlands Programme I

What is the Langlands Programme II

What is the Langlands Programme III

What is the Langlands Programme IV

What is the Langlands Programme V

What is the Langlands Programme VI

What is the Langlands Programme VII

What is the Langlands Programme VIII

What is the Langlands Programme IX

What is the Langlands Programme X

What is the Langlands Programme XI

Building up spacetime with quantum entanglement

Japanese version
The following essay is very comprehensive to understand how to emerge timespace from entanglement entropy. The original is on arxiv:1005.3035 titled "Building up spacetime with quantum entanglement." I had translated it into Japanese.

Building up spacetime with quantum entanglement (in English)

Building up spacetime with quantum entanglement (in Japanese)

In particular, Entanglement entropy is closely related with quantum gravity theory, the theory of black holes and entropic gravity theory, talked by E. Verlinde and A Strominger, I think.

4d QFT for Khovanov Homology

Japanese version
In the end of Feb. 2011 there was an very interesting article titled "4d QFT for Khovanov Homology," which contains some discussions about Witten's paper "Fivebranes and knots"titled. So I have translated into Japanese.

the original article on n-cafe:

4d QFT for Khovanov Homology (in English)

And I had tried to explain a little but all are in Japanese only.

1,Its translation
4d QFT for Khovanov Homology (in Japanese)

2,Atiyah asked why the coefficients of Jones polynomial is integers. Not on a paper but on slide by S. Gukov this episode appeared.
an episode on Khovanov Homology (in Japanese only)

3,Atiyah-Floer conjecture in Gukov's paper Gukov on categorification and gauge theory along Ben Webster's Blog.
an episode on Khovanov Homology I (in Japanese only)

3,Casson invariants is very important in categorification refering to Ben Webster's Blog.
an episode on Khovanov Homology II (in Japanese only)

4,What is oroginally Khovanov homology? an introduction to Khovanov homology.
an episode on Khovanov Homology III (in Japanese only)

On Gravitational Instanton

Japanese version
I will translat into Japanese the article titled "Gravitational Instanton" on en.wiki. Because there are no article titled so on Japanese version. The original is the following:

Gravitational Instanton

translation into Japanese:

Gravitational Instanton(in Japanese)

Mahler’s measure, hyperbolic geometry and the dilogarithm

Japanse version
Dr. David Boyd was a professor of Number Theory at British Columbia UNIV. for a long time. I had recently known his retirement. About 9 years ago I read his article on a journal and write it 1page as "shakyoh," which means copying the bible of Buddhism in Japan. After his retirement I knew the article remained on the net. And, the full text was able to be acquired. There is Nunber Theory to run freely about three fields of mathematics of algebra, geometry, and the analysis. I translated into the full text Japanese and to post it on my BLOG. It is fortunate if becoming a part of the motive of a young person.

The original articles are on p3,p4,p26,p27,p28 of the following journal:

Mahler's measure, hyperbolic geometry and the dilogarithm

and p15,p16 of the following journal:

Explicit formulas for Mahler measure

Its translation is decomposed to three parts.

Mahler's measure, hyperbolic geometry and the dilogarithm I (in Japanese)

Mahler's measure, hyperbolic geometry and the dilogarithm II (in Japanese)

Mahler's measure, hyperbolic geometry and the dilogarithm III (in Japanese only, my comments or explanation)

Mahler's measure, hyperbolic geometry and the dilogarithm IV (in Japanese) corresponding to "Explicit formulas for Mahler measure"

Mahler's measure, hyperbolic geometry and the dilogarithm V (in Japanese only, my comments or explanation)

"The Holographic Universe" on FQXi

Japanese version
I had traslated the article on FQXi tiled "he Holographic Universe" about Dr. Maloney. But I had changed a liitle the title by "wave functions on de Sitter spaces," and posted my BLOG. This article is related to the paper of Dr. Strominger titled "Five problems on Quantum Gravity."

the original article :
The Holographic Universe (in English)

the translation :

The Holographic Universe (in Japanese)

"Dr. Hawking’s bright idea" on The Economist

Japanese version
I had translated into Japanese the article on The Economist in 29 Sep. 2011. On the headline of the article is "Mimicking black holes."

The original :
Dr. Hawking's bright idea (in English)

its translation :

Dr. Hawking's bright idea (in Japanese)

Theory of Black Holes

Japanese version
1, Some elementary explanation of general relativity and black holes

General Relativity and Black Holes

General Relativity and Black Holes II

2, Prof. Strominger's paper:
Five Problems in Quantum Gravity

3, articles on News Papers and so on.
"Dr. Hawking's bright idea" on The Economist

"The Holographic Universe" on FQXi

"Viewpoints on String Theory" on PBS

A glossary of physics on PBS with links to en.wiki
This glossary is quoted in "Viewpoints on String Theory" on PBS.

Entropic Gravity

Japanese version
1, A plane explanation for what is his cosmological spectacle.

Topics apperaring in E. Verlinde's lecture I

Topics apperaring in E. Verlinde's lecture II

Topics apperaring in E. Verlinde's lecture III

Topics apperaring in E. Verlinde's lecture IV

The lecture by E. Verlinde in Uppsala at Strings 2011

The lecture by E.Verlinde in Uppsala at String 2011

The lecture by E.Verlinde at Perimeter Inst. My simple document about Verlinde's lecture and its movie.

The lecture by E.Verlinde at Perimeter Inst.

2, Entropic Gravity and Cosmology

An interview article by the Danish science writer Robin Englhardt:

Erik Verlinde, the Big Bang and a new Explanation of the Universe

The Japanese translation by me:

Erik Verlinde, the Big Bang and a new Explanation of the Universe (in Japanese)

28 Apr. 2011 Dr. E. Verlinde gave a Lecture at CERN Colloquium. In 2010 He proposed that the string duality and the holographic principle are given by the adiabatic theorem of thermodynamics at Harvard Lecture and at KITP. And I think that Dark matter, Dark energy and Matter are considered from the this point of views. For general audience the above interview article is closely related to the Lecture at CERN.

The slide of Lecture:

THE COMMON ORIGIN OF GRAVITY DARK ENERGY AND MATTER

3, An article on newspaper

A new view of Gravity

A small movie of Entropic Gravity

4, Some lectures by E. Verlinde on entropic gravity theory

At Harvard Univ at Sep. 2010
Emergency of Gravity

At KITP at Aug. 2010
Emergency of Gravity

A small movie of Entropic Gravity

Japanese version
Futhur, at Aug. 2010 I translate into Japanese the interview article on Big Think titled "Gravity Doesn't Exist." This article is contained the following URL:

Gravity Doesn't Exist

In Japanese:

non titled (in Japanese)

A new view of Gravity

Japanese version
In my Japanese BLOG, the most popular post is "A New View of Gravity" at Sep. 29 2010, which is also translated from the article on ScienceNews, whose original URL is:

A New View of Gravity (in English)

In Japanese:

A New View of Gravity (in Japanese)

Five Problems in Quantum Gravity (translation)

Japanese version
Professor A. Strominger published "Five Problems in Quantum Gravity" on Nuclear Phsics B (2009) 119-125 (its preprint is arxiv:0906.1313). I think that in this paper it is very clear to point out the problem of quantum gravity. And I translated it into Japanese.

Five Problems in Quantum Gravity

Four reasons why I like string theory

Japanese version
Mr. Phil Gibbs had written an article titled "Four reasons why I like string theory" as a guest post on Mr. Lubos Motl's BLOG "the reference frame" at this 26 Feb.. It is very interesting for me though I don't have the same opinion about string theory. And I translated into Japanese.

Four reasons why I like string theory (in English)

Entropic Gravity and Cosmology

Japanese version
Just one year ago, I knew the paper of Dr. Erik Verlinde on Entropic Gravity. Then I read it with much interest and post some article on newspaper and so on translated into Japanese. Now, recently I have focus to the CERN lecture titled ""On the Origin of Gravity, Dark Energy and Matter." But I could neither go to CERN nor get the slide of it. Instead, I translated an interview article on Robin Englhardt's BLOG, which is titled "Erik Verlinde, the Big Bang and a new Explanation of the Universe." It is a very nice article and explains simply this subject.

Erik Verlinde, the Big Bang and a new Explanation of the Universe

The Japanese version is the following, which is divided into three parts.

The Big Bang and a new Explanation of the Universe I

The Big Bang and a new Explanation of the Universe II

The Big Bang and a new Explanation of the Universe III