### 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. Fundamentals of Quantum Complex Action Theory Keiichi Nagao and Holger Bech Nielsen Lambert Academic Publishing 2017/09/27 978-3-330-08445-2 URL Quantum theory is formulated via the Feynman path integral, where only a past state is given at first. We could consider another formulation, where both past and future states are provided. In addition, an action is usually taken to be real, but there is a possibility that the action is complex at the fundamental level. Thus, quantum theory can be classified into four types, according to whether the future is included or not, and whether the action is real or not. In this book we present our fundamental formulation of the quantum complex action theory. We introduce various mathematical devices, which do not appear in usual textbooks of quantum mechanics, and argue that we cannot exclude the future-included complex action theory, though such a theory looks very exotic. Furthermore, we discuss how we can obtain Hermitian Hamiltonians and real observables. We concentrate on quantum theory having only one degree of freedom, i.e., quantum mechanics in just one dimensional space. Therefore, this book would be suitable for not only researchers and graduate students of physics and mathematics but also undergraduate students who learned quantum mechanics.
2. 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
3. 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）
4. 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 Erratum: Theory including future not excluded: Formulation of complex action theory II" Keiichi Nagao, Holger Bech Nielsen Progress of Theoretical and Experimental Physics 2018/ 3, 039201-1-039201-2 2018/03/27 10.1093/ptep/pty023 URL
2. 研究論文（学術雑誌） 共著 Erratum: Momentum relation and classical limit in the future-not-included complex action theory" Keiichi Nagao, Holger Bech Nielsen Progress of Theoretical and Experimental Physics 2018/ 2, 029201-1-029201-1 2018/02/15 10.1093/ptep/ptx176 URL
3. （MISC）総説・解説（大学・研究所紀要） 単著 小学校理科における「電磁石の性質」についての実験の現状と課題 永尾 敬一 茨城大学教育学部紀要（教育科学） 67, 135-145 2018/01/30 URL 茨城県教育委員会は，いばらき理科教育推進事業の一環として，小学校教員の理科の指導力を高めることを目的として，推進地域モデル小学校公開授業研究会を実施してきた。その内容は，授業の公開と研究協議，そして，茨城大学教員による助言と指導である。私は，単元名「電磁石の性質」についての公開授業研究会に，平成 23 年から毎年，通算で6 回参加してきた。本稿では，現場の様子を報告するとともに，現場で気づいた課題の改善方法を提案する。
4. 研究論文（国際会議プロシーディングス） 共著 Reality from maximizing overlap in the future-included theories Keiichi Nagao and Holger Bech Nielsen Bled Workshops in Physics (Proceedings to the 20th workshop "What Comes Beyond the Standard Models", Bled, Slovenia, Jul.9-17, 2017) DMFA 18/ 2, 121-132 2017/12/12 1580-4992 URL In the future-included complex and real action theories whose paths run over not only the past but also the future, we briefly review the theorem on the normalized matrix element of an operator $\hat{\cal O}$, which is defined in terms of the future and past states with a proper inner product $I_Q$ that makes a given Hamiltonian normal. The theorem states that, provided that the operator $\hat{\cal O}$ is $Q$-Hermitian, i.e. Hermitian with regard to the proper inner product $I_Q$, 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. Discussing what the theorem implicates, we speculate that the future-included complex action theory would be the most elegant quantum theory.
5. 研究論文（学術雑誌） 共著 Complex action suggests future-included theory Keiichi Nagao and Holger Bech Nielsen Progress of Theoretical and Experimental Physics Oxford University Press 2017/ 11, 111B01-1-111B01-9 2017/11/23 10.1093/ptep/ptx156 URL In quantum theory its action is usually taken to be real, but we can consider another theory whose action is complex. In addition, in the Feynman path integral, the time integration is usually performed over the period between the initial time $T_A$ and some specific time, say, the present time $t$. Besides such a future-not-included theory, we can consider the future-included theory, in which not only the past state $| A(T_A) \rangle$ at the initial time $T_A$ but also the future state $| B(T_B) \rangle$ at the final time $T_B$ is given at first, and the time integration is performed over the whole period from the past to the future. Thus quantum theory can be classified into four types, according to whether its action is real or not, and whether the future is included or not. We argue that, if a theory is described with a complex action, then such a theory is suggested to be the future-included theory, rather than the future-not-included theory. Otherwise persons living at different times would see different histories of the universe.

#### 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]))

1. 物理学概論
2. 物理学特論
3. 初等理科内容研究
4. 初等自然科学総合研究
5. 中等自然科学総合研究

#### 社会貢献活動

1. 平成２９年度小学校理科教育推進事業「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＠鉾田市立鉾田小学校 2017/10/26-2017/10/26 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、鉾田市立鉾田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。
2. 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。
3. 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。
4. 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。
5. 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。

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