Sunday, November 27, 2011

A translation of "Why do we expect a Higgs boson? Part I: Electroweak Symmetry Breaking" on QuantumDiaries.

Japanese version
I complete to translate the very nice article by US LHC Mr. Flip Tanedo on Quantum Diary, titled "Why do we expecy a Higgs boson? Part I: Electroweak Symmetry Breaking" and post it my BLOG.

The spontanuously electroweak symmetry spontaneously breaking is very important.

A Japanese translation:

Why do we expecy a Higgs boson? Part I: Electroweak Symmetry Breaking (only Japanese version)


The original article on QuantumDiaries:

Why do we expecy a Higgs boson? Part I: Electroweak Symmetry Breaking

Saturday, November 26, 2011

Some Lecture notes by Dr. Sarnak

Japanese version
Mr. Woit's blog was introduced ignited by Dr. Witten's lecture at IAS for general: "Knots and Quantum Theory." About physics and arithmetic, Dr. Witten might say that there would be a bridge between Number Theory and Physics. Of course, the keyword is Langlands. The magazine "arithmetic and physics" (I'm forgotten the formal name of English journal) is started, and the first publication and the leadoff article are Witten-Kapustin. Indeed!

Dr. Sarnak's lecture note contains Selberg 1/4 conjecture, general Ramanujan anticipation, etc. about which are argued on Woit's Blog.report. The following lecture notes by Dr. Sarnak are not familiar in Japan.

1,"Arinthmetic Quantum Chaos"

2,"Selberg eigenvalue problems"

3,"The generalized Ramanujan conjecture"

4,"Spectra of hyperbolic surfaces"

the above item 4 had not come out in Woit's BLOG but I think it is a very interesting and exiting note and let me it join to others. It is pointing the direction of "physics and arithmetic." Its contents are:

1,Introduction
2,Existence
3,High Energy Spectrum
4,Low Energy Spectrum


In 2004 Dr. Sarnak published a article about Riemann Hypothesis on Claymath Instiute.
Problems of the Millennium: The Riemann Hypothesis (2004)

May/27/2011 added:
In 1993 Dr. Sarnak had proved the analogy of Shimura correspondense for Maass forms (with SVETLANA KATOK).

HEEGNER POINTS, CYCLES AND MAASS FORMS

Wednesday, November 23, 2011

From Woit's BLOG "Knots and Quantum Theory"

Japanese version
In October 28, 2011 E.Witten gave the lecture for general "Knot and Quantum Theory." Although backgrounds are Khovanov homology and quantum field theory, the talk included Langlands crrespondence (in usual in Number Theory), and they have taken the attention by some BLOG, which he might think in mind on the relations between physics and number theory. I complete to translate almost of Woit's BLOG with comments into Japanese and post it. The argument still continues.

From Woit's BLOG "Knots and Quantum Theory" (in Japanese only)

P. Woit's original BLOG:
Knots and Quantum Theory
E.Witten's lecture:
Knots and Quantum Theory

Saturday, November 12, 2011

The appendix of "Stefan Boltzmann law"

Japanese version
The special value of the Zeta function is important for the law of Planck, and the same thing is important also for the law (the energy distribution of black body radiation is proportional to the 4-th power of absolute temperature) of Boltzmann. From the formula of Planck, the law of Boltzmann can be drawn and it is in agreement with the observed value in experiments.

The Zeta function appears similarly in these derivation processes, this is indicated as the appendix of the article "Stefan Boltzmann law" in en.Wikipedia in English. Since there was no description of them in Japanese version, I translate it into Japanese.
The original article:
Stefan–Boltzmann law

a Japanese translation of the appendix of "Stefan-Boltzmann law":
The Appendix of "Stefan–Boltzmann law" (in Japanese)

Friday, November 11, 2011

The appendix of "Planck's law"

Japanese version
In 1900, M. Planck pointed out the breakdown of classical electrodynamics. That is because the energy density per unit volume becomes infinite and is not in agreement with an experiment in classical electrodynamics. The formula that on the other hand the energy distribution of the spectrum radiation luminosity of the electromagnetic waves radiated from the black body called the law of Planck becomes limited from the thermodynamic view submitted by Boltzmann is drawn. This was taken over to the light(energy)-quantum theory of Einstein on the assumption that e=hv, and it paved the way for quantum mechanics. In calculation of this energy density, the fact which is a limited value which the special value of the Zeta function of Riemann can calculate appears.

Although there is a statement of a method which uses the special value of a Riemann Zeta function for the supplement of the item of "the law of Plank" of Japanese wikipedia, since this is not indicated to an English-language edition, it translates into English.

The Appendix of "Planck's law"

Sunday, November 6, 2011

Zeta Functions and Statistical Dynamics (Seminar) VI

Japanese version
In 23 Oct.2011 Mathematical Physics Seminar the second I gave a talk about "Zeta Functions and Statistical Dynamics," And now as the last part VI "Appendix a story of (thermo) statistical dynamics" is posted.

The contents are the following :

0,Introduction

1,Distribution of prime numbers (Riemann zeta function)

2,The origin of conjunction of Phys. and NT.

3,Various zeta functions

4,Statistical Dynamics and Zeta Functions

App. A story of (Thermo) Statistical Dynamics

Zeta Functions and Statistical Dynamics VI appendix

Saturday, November 5, 2011

Zeta Functions and Statistical Dynamics (Seminar) V

Japanese version
In 23 Oct.2011 Mathematical Physics Seminar the second I gave a talk about "Zeta Functions and Statistical Dynamics," And now as part V "4,Statistical Dynamics and Zeta Functions (the later part)" is posted. I mention the relation between Riemann zeta and Hagedorn temperature, Pauli exclusive principle, and Bose-Einstein condensation, and Lee-Yang theorem.

The contents are the following :

0,Introduction

1,Distribution of prime numbers (Riemann zeta function)

2,The origin of conjunction of Phys. and NT.

3,Various zeta functions

4,Statistical Dynamics and Zeta Functions

App. A story of (Thermo) Statistical Dynamics

Zeta Functions and Statistical Dynamics IV B

Zeta Functions and Statistical Dynamics (Seminar) IV

Japanese version
In 23 Oct.2011 Mathematical Physics Seminar the second I gave a talk about "Zeta Functions and Statistical Dynamics," And now as part IV "4,Statistical Dynamics and Zeta Functions (the previous part)" is posted. I mention arithmetic functions and its connection to statistic dynamics, in particular "When did Zeta function connect to (thermo) statistical dynamics?"

The contents are the following :

0,Introduction

1,Distribution of prime numbers (Riemann zeta function)

2,The origin of conjunction of Phys. and NT.

3,Various zeta functions

4,Statistical Dynamics and Zeta Functions

App. A story of (Thermo) Statistical Dynamics

Zeta Functions and Statistical Dynamics IV A

Thursday, November 3, 2011

Zeta Functions and Statistical Dynamics (Seminar) III

Japanese version
In 23 Oct.2011 Mathematical Physics Seminar the second I gave a talk about "Zeta Functions and Statistical Dynamics," And now as part III "3,Various zeta functions" is posted. I mention congruent zeta and Selberg zeta and various conjecture of quantum chaos. My talk is related Mr. Konishi's at the first seminar.

The contents are the following :

0,Introduction

1,Distribution of prime numbers (Riemann zeta function)

2,The origin of conjunction of Phys. and NT.

3,Various zeta functions

4,Statistical Dynamics and Zeta Functions

App. A story of (Thermo) Statistical Dynamics

Zeta Functions and Statistical Dynamics III

Zeta Functions and Statistical Dynamics (Seminar) II

Japanese version
In 23 Oct.2011 Mathematical Physics Seminar the second I gave a talk about "Zeta Functions and Statistical Dynamics," And now as part II "2,The origin of conjunction of Phys. and NT." is posted. The talk is related Mr. Konishi's talk at the first seminar.

The contents are the following :

0,Introduction

1,Distribution of prime numbers (Riemann zeta function)

2,The origin of conjunction of Phys. and NT.

3,Various zeta functions

4,Statistical Dynamics and Zeta Functions

App. A story of (Thermo) Statistical Dynamics

Zeta Functions and Statistical Dynamics II