### 永尾　敬一

ナガオ　ケイイチ
NAGAO Keiichi

#### 経歴

1. 高エネルギー加速器研究機構　素粒子原子核研究所　協力研究員 2002/04-2003/01
2. 高エネルギー加速器研究機構　素粒子原子核研究所　研究機関研究員 2003/01-2005/03
3. 茨城大学　教育学部　理科教育教室　助教授 2005/04/01-2007/03/31
4. 茨城大学　教育学部　理科教育教室　准教授 2007/04/01-現在

#### 学歴

1. 東京大学 総合文化研究科 広域科学専攻　相関基礎科学系 博士 2002 修了
2. 東京大学 総合文化研究科 広域科学専攻　相関基礎科学系 修士 1999 修了
3. 東京大学 理学部 物理学科 1997 卒業

#### 学位

1. 学術修士 東京大学 1999/03
2. 学術博士 東京大学 2002/03

#### 研究分野

1. 素粒子・原子核・宇宙線・宇宙物理

#### 研究テーマ

1. 超弦理論および量子重力理論の非摂動論的研究 2002-現在

#### 著書

1. ゲルダ・シュタイナー&ヨルク・レンツリンガー - 力が生まれるところ 門脇さや子編 水戸芸術館現代美術センター 2012/03/31 9784943825982 水戸芸術館現代美術センター展覧会資料, 第96号
2. 理科実験大百科 第10集 少年写真新聞社 2010/02 978-4879813312 素粒子の話（SPP事業教員研修）
3. Lattice QCD with the Overlap Fermions at Strong Gauge Coupling Ikuo Ichinose, Keiichi Nagao Dynamics of gauge fields: TMU-Yale Symposium 2000/05 9784946443589 Proceedings of TMU-Yale Symposium on the Occasion of TMU's 50th anniversary held on December 13-15, 1999 at Tokyo Metropolitan University, Japan

#### 論文

1. 研究論文（学術雑誌） 共著 Reality from maximizing overlap in the future-included real action theory Keiichi Nagao and Holger Bech Nielsen Progress of Theoretical and Experimental Physics Oxford University Press 2017/ 8, 081B01, 1-8 2017/08/01 10.1093/ptep/ptx102 In the future-included real action theory whose path runs over not only past but also future, we demonstrate a theorem, which states that the normalized matrix element of a Hermitian operator $\hat{\cal O}$ defined in terms of the future state at the final time $T_B$ and the fixed past state at the initial time $T_A$ becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory.
2. 研究論文（学術雑誌） 共著 Reality and hermiticity from maximizing overlap in the future-included complex action theory Keiichi Nagao and Holger Bech Nielsen Progress of Theoretical and Experimental Physics Oxford University Press 2015/ 5, 051B01, 1-9 2015/05/11 10.1093/ptep/ptv057 In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator $\hat{\cal O}$ defined in terms of the future state at the latest time $T_B$ and the past state at the earliest time $T_A$ with a proper inner product that makes normal a given Hamiltonian that is non-normal at first. We present a theorem that states that, provided that the operator $\hat{\cal O}$ is $Q$-Hermitian, i.e., Hermitian with regard to the proper inner product, the normalized matrix element becomes real and time-develops under a $Q$-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the $Q$-Hermitian Hamiltonian in terms of $Q$-Hermitian coordinate and momentum operators, and construct a conserved probability current density.
3. 研究論文（学術雑誌） 共著 Momentum relation and classical limit in the future-not-included complex action theory Keiichi Nagao and Holger Bech Nielsen Progress of Theoretical and Experimental Physics Oxford University Press 2013/ 7, 073A03, 1-22 2013/07/01 10.1093/ptep/ptt047 Studying the time development of the expectation value in the future-not-included complex action theory, we point out that the momentum relation (the relation analogous to $p=\frac{\partial L}{\partial \dot{q}}$), which was derived via the Feynman path integral and was shown to be correct in the future-included theory in our previous papers, is not valid in the future-not-included theory. We provide the correct momentum relation in the future-not-included theory, and argue that the future-not-included classical theory is described by a certain real action. In addition, we provide another way to understand the time development of the future-not-included theory by utilizing the future-included theory. Furthermore, properly applying the method used in our previous paper to the future-not-included theory by introducing a formal Lagrangian, we derive the correct momentum relation in the future-not-included theory.
4. 研究論文（学術雑誌） 共著 Theory Including Future Not Excluded :　Formulation of Complex Action Theory II Keiichi Nagao and Holger Bech Nielsen Prog. Theor. Exp. Phys. Oxford University Press 2013/ 2, 023B04, 1-21 2013/02/04 10.1093/ptep/pts084 We study a complex action theory (CAT) whose path runs over not only past but also future. We show that, if we regard a matrix element defined in terms of the future state at time T_B and the past state at time T_A as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, Ehrenfest's theorem, and the conserved probability current density. In addition, we show that the expectation value at the present time t of a future-included theory for large T_B − t and large t − T_A corresponds to that of a future-not-included theory with a proper inner product for large t − TA. Hence, the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore, we explicitly derive the Hamiltonian for the future state via a path integral, and confirm that it is given by the Hermitian conjugate of the Hamiltonian for the past state.
5. （MISC）総説・解説（国際会議プロシーディングズ） 共著 Correspondence between future-included and future-not-included theories Keiichi Nagao and Holger Bech Nielsen Proceedings to the 15th workshop What Comes Beyond the Standard Models", Bled, Slovenia, Jul.9-19, 2012 86-93 2012/12 1580-4992 We briefly review the correspondence principle proposed in our previous paper, which claims that if we regard a matrix element defined in terms of the future state at time $T_B$ and the past state at time $T_A$ as an expectation value in the complex action theory whose path runs over not only past but also future, the expectation value at the present time $t$ of a future-included theory for large $T_B-t$ and large $t-T_A$ corresponds to that of a future-not-included theory with a proper inner product for large $t-T_A$. This correspondence principle suggests that the future-included theory is not excluded phenomenologically.

#### 研究発表

1. 口頭発表（一般） Reality from maximizing overlap in the future-included real action theory 日本物理学会2017年秋季大会 2017/09/12 In the future-included real action theory whose path runs over not only past but also future, we demonstrate the theorem, which states that the normalized matrix element of a Hermitian operator !LaTeX$\hat{O}$ defined in terms of the future state at the final time T_B and the fixed past state at the initial time T_A becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory.
2. 口頭発表（一般） Reality from maximizing overlap in the future-included real action theory 茨城大学理学部素粒子論研究室セミナー 2017/06/12 In the future-included real action theory whose path runs over not only past but also future, we demonstrate the theorem, which states that the normalized matrix element of a Hermitian operator O defined in terms of the future state at the final time T_B and the fixed past state at the initial time T_A becomes real for the future state selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. This is a special version of our previously proposed theorem for the future-included complex action theory. We find that though the maximization principle leads to the reality of the normalized matrix element in the future-included real action theory, it does not specify the future and past states so much as in the case of the future-included complex action theory. In addition, we argue that the normalized matrix element seems to be more natural than the usual expectation value. Thus we speculate that the functional integral formalism of quantum theory could be most elegant in the future-included complex action theory. This talk is based on the collaboration with Holger Bech Nielsen (arXiv:1705.01585 [quant-ph]).
3. 口頭発表（一般） Reality and hermiticity from maximizing overlap in the future-included complex action theory Theoretical High Energy Seminar @NBI 2017/02/09 In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator O defined in terms of the future state at the latest time TB and the past state at the earliest time TA with a proper inner product which makes a non-normal Hamiltonian at first given normal. We present a theorem which states that provided that the operator O is Q-Hermitian, i.e. Hermitian with regard to the proper inner product the normalized matrix element becomes real and time-develops under a Q-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the Q-Hermitian Hamiltonian in terms of Q-Hermitian coordinate and momentum operators, and construct a conserved probability current density. This talk is based on the collaboration with Holger Bech Nielsen (Prog.Theor.Exp.Phys.(2015)051B01(arXiv:1502.00385[quant-ph])).
4. 口頭発表（一般） Expression of the Q operator for the proper inner product in complex harmonic oscillator 日本物理学会2015年秋季大会 2015/09/16 複素作用理論においてはハミルトニアンがエルミートでないため、その固有状態は互いに直交しないが、固有状態が互いに直交するような修正された内積をエルミートな演算子Qを用いて導入することができる。本講演では、調和振動子模型の場合において、二種類の生成・消滅演算子を定式化するなどして、そのような演算子Qの具体形を導出する。
5. 口頭発表（一般） Reality and hermiticity from maximizing overlap in the future-included complex action theory 日本物理学会2015年秋季大会 2015/09/16 In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator O defined in terms of the future state at the latest time $T_B$ and the past state at the earliest time $T_A$ with a proper inner product that makes normal a given Hamiltonian that is non-normal at first. We present a theorem that states that, provided that the operator O is Q-Hermitian, i.e., Hermitian with regard to the proper inner product, the normalized matrix element becomes real and time-develops under a Q-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the Q-Hermitian Hamiltonian in terms of Q-Hermitian coordinate and momentum operators, and construct a conserved probability current density. (Ref:PTEP(2015)051B01(arXiv:1502.00385[quant-ph]))

#### 芸術活動、建築作品等

1. その他 単独 平成20年度　特定国派遣研究者 2008/04/01-2008/09/26 背景独立な行列模型およびループ重力におけるカイラルフェルミオンの定式化の研究

#### 社会貢献活動

1. 平成２９年度小学校理科教育推進事業「科学自由研究の指導(探究基礎)」夏休み科学自由研究相談会＠茨城県女性プラザ 2017/07/31-2017/07/31 茨城県教育委員会との連携事業（小学校理科教育推進事業「理科授業の質の向上」）の一環として、茨城県女性プラザで開催された夏休み科学自由研究相談会において、指導と助言を行なった。
2. 平成２８年度小学校理科教育推進事業「理科授業の質の向上」推進地域モデル小学校公開授業研究会＠鹿嶋市立中野西小学校 2016/11/15-2016/11/15 茨城県教育委員会との連携事業（小学校理科教育推進事業「理科授業の質の向上」）の一環として、鹿嶋市立中野西小学校で開催された研究協議会において、指導と助言を行なった。
3. 平成２８年度いばらき理科教育推進事業「科学自由研究の指導(活用・発展)」ミニ博士によるミニ学会＠ミュージアムパーク茨城県自然博物館 2016/10/23-2016/10/23 茨城県教育委員会との連携事業（いばらき理科教育推進事業「科学自由研究の指導(活用・発展)」）の一環として、ミュージアムパーク茨城県自然博物館で開催されたミニ博士によるミニ学会において、指導と助言を行なった。
4. 平成２８年度小学校理科教育推進事業「科学自由研究の指導(探究基礎)」夏休み科学自由研究相談会＠茨城県女性プラザ 2016/08/01-2016/08/01 茨城県教育委員会との連携事業（小学校理科教育推進事業「理科授業の質の向上」）の一環として、茨城県女性プラザで開催された夏休み科学自由研究相談会において、指導と助言を行なった。
5. 平成２７年度いばらき理科教育推進事業「科学自由研究の指導(活用・発展)」ミニ博士によるミニ学会＠ミュージアムパーク茨城県自然博物館 2015/10/25-2015/10/25 茨城県教育委員会との連携事業（いばらき理科教育推進事業「科学自由研究の指導(活用・発展)」）の一環として、ミュージアムパーク茨城県自然博物館で開催されたミニ博士によるミニ学会において、指導と助言を行なった。

1. 日本物理学会

#### 委員歴

1. 茨城県教育委員会 平成29年度 科学の甲子園ジュニア実行委員 2017/05/12-現在