Fumio Hiroshima | Last modified date：2024.04.04 |

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Reseacher Profiling Tool Kyushu University Pure

Academic Degree

Doctor of science

Country of degree conferring institution (Overseas)

Yes Doctor

Field of Specialization

Analysis

ORCID(Open Researcher and Contributor ID)

0000-0002-3435-9957

Total Priod of education and research career in the foreign country

02years06months

Outline Activities

We study spectral analysis of operators on infinite dimensional spaces. In particular, We analyze the spectral analysis of quantum field theory on pseudo-Riemannian manifolds from a mathematical standpoint, using operator theory, the theory of semigroups, stochastic analysis, and functional and path integrals. The Hamiltonian appearing in quantum field theory can be regarded mathematically as a self-adjoint operator on a Hilbert space. The spectrum of the self-adjoint operator is analyzed in a non-perturbative and abstract way.

Specifically, our goals are to evaluate the existence or absence of the ground state of the Hamiltonian, to analyze IR and UV divergences, spectral scattering theory, resonance, renormalization theory, Gibbs measure, and so on. Recently, We have also studied the representation theory of CCR and lattice Schrödinger operators. The keywords are Feynman-Kac formula, quantum field theory, Gibbs measure, renormalization, spectral analysis, Schrödinger operator, boson-Fock space, infinite-dimensional Ornstein-Uhlenbeck process, exponential decay property, Gaussian decay property, UV divergence, IR divergence, existence and absence of ground states, semigroups, noncommutative Perron-Frobenius theorem, Kato potential, Bernstein function, Pauli-Fierz model, Nelson model, spin-boson model, noncommutative harmonic oscillator (NCHO), Rabi model, spectral zeta function, time operator, CCR, Laplacian on a lattice, semi-classical analysis.

Specifically, our goals are to evaluate the existence or absence of the ground state of the Hamiltonian, to analyze IR and UV divergences, spectral scattering theory, resonance, renormalization theory, Gibbs measure, and so on. Recently, We have also studied the representation theory of CCR and lattice Schrödinger operators. The keywords are Feynman-Kac formula, quantum field theory, Gibbs measure, renormalization, spectral analysis, Schrödinger operator, boson-Fock space, infinite-dimensional Ornstein-Uhlenbeck process, exponential decay property, Gaussian decay property, UV divergence, IR divergence, existence and absence of ground states, semigroups, noncommutative Perron-Frobenius theorem, Kato potential, Bernstein function, Pauli-Fierz model, Nelson model, spin-boson model, noncommutative harmonic oscillator (NCHO), Rabi model, spectral zeta function, time operator, CCR, Laplacian on a lattice, semi-classical analysis.

Research

**Research Interests**

- semiclassical analysis

keyword : Wigner measure, Pauli-Fierz model

2019.05～2022.12. - Spectral analysis of QFT

keyword : quantum field theory, Fock space, embedded eigenvalues, ground states, scattering theory, pseudo Riemann manifold, resonances, renormalization group, functional integrations, Gibbs measures

1993.04. - Feynman-Kac formula and related topics

keyword : Schroedinger operator, relativistic Schroedinger operator, Schroedinger operator with spin, relativistic Schroedinger operator with spin, PF model, Nelson model, spin-boson model

2006.04. - Gibbs measure and localizations

keyword : Gibbs measure, ground states, UV renormalization, exponential decay

2000.04. - Spectral zeta functions

keyword : Rabi model, non-commutative harmonic oscillator

2013.04. - Time operators and CCR representations

keyword : time operator, CCR

2009.04. - Schrodinger operator on lattice

keyword : lattice, spectrum

2012.04.

**Academic Activities**

**Books**

**Reports**

**Papers**

**Presentations**

1. | Fumio Hiroshima, Asymmetry of non-local discrete Schroedinger operators on a lattice, Mathematical Analysis and its Applications in Modern Mathematical Physics, 2022.09. |

2. | Fumio Hiroshima, Semi-classical analysis in quantum field theory, The 43-rd International Conference on Quantum Probability and Infinite Dimensional Analysis, 2023.01. |

3. | Fumio Hiroshima, Angle operators and phase operators associated with 1D-harmonic oscillator , A quantum two-day meeting with Green talks, Green functions, and threshold behavior, 2022.04. |

4. | 廣島文生, Localization of the ground state of the Nelson model, Himeji conference on PDE, 2021.03. |

5. | Fumio Hiroshima, Localizations of bound states of a renormalized Hamiltonian, Scattering, microlocal analysis and renormalisation,Mittag-Leffler Institute, Stockholm, 2020.06. |

6. | Fumio Hiroshima, Semi-classical analysis and Wigner measure for non-relativistic QED, NAKAMURA60, Gakushuin univ. , 2020.01. |

7. | Fumio Hiroshima, Stochastic renormalization, MSJ, Nippon univ. , special lecture, 2019.09. |

8. | Fumio Hiroshima, Hierarchy of CCR representations, Aarhus university, seminar, Denmark, 2018.10. |

9. | Fumio Hiroshima, Integral kernels of semigroup generated by a model in quantum field theory, 18th Workshop: Noncommutative Probability, Operator Algebras, Random Matrices and Related Topics, with Applications,Bedlewo, Poland, 2018.07. |

10. | Fumio Hiroshima, Ground state of renormalized Nelson model, Aarhus university, Math. Phys. seminar, Denmark, 2017.12. |

11. | Fumio Hiroshima, Schroedinger operators on lattice, Second Summer School: Various aspects of mathematical physics,St Petersburg,Russia, 2017.07, [URL]. |

12. | Fumio Hiroshima, Feynman-Kac formula and its application to quantum physics, Mathematical Analysis of Interacting Quantum Systems, Rennes univ., France, 2017.03. |

13. | Fumio Hiroshima, Analysis of time operators, La Sapienza univ. Math. Phys. seminar, Rome, 2017.02. |

14. | Fumio Hiroshima, Time operator associated with Schroedinger operators, QUTIS, Bilbao, Spain, 2016.09. |

15. | Fumio Hiroshima, Threshold ground state of the semi-relativistic Pauli-Fierz Hamiltonian,Aarhus university, Aarhus univ. Seminar, Denmark, 2016.02. |

16. | Fumio Hiroshima, Stochastic analysis of quantum field theory, MSJ, Kyoto Ind. univ. , special lecture, 2015.09. |

17. | Fumio Hiroshima, Analysis of ground state of quantum field theory by Gibbs measures, International Congress of Mathematical Physics(ICMP) 2015,Chile, 2015.08. |

18. | Fumio Hiroshima, Spectrum of semi-relativistic QED by a Gibbs measure, The 51 winter school of theoretical physics (Karpacz Winter Schools in Theoretical Physics), Poland, 2015.02. |

19. | Fumio Hiroshima, Functional integral approach to mathematically rigorous quantum field theory, TJASSST2013, Tunisia, 2013.11. |

20. | Fumio Hiroshima, Gibbs measure approach to spin-boson model, International conference on stochastic analysis and applications, Tunisia, 2013.10. |

21. | Fumio Hiroshima, Non-relativistic QFT and Gibbs measures, math and phys summer school lecturer, Univ. Tokyo, 2013.09. |

22. | Fumio Hiroshima, Spectrum of non-commutative harmonic oscillator and related models, Bologna univ. seminar, Italy, 2013.09. |

23. | Fumio Hiroshima, Enhanced binding for quantum field models, Universite de Rennes 1 seminar, France, 2013.03. |

24. | Fumio Hiroshima, Gibbs measure approach to properties of ground state in QFT, Laboratoire d’Analyse,Topologie,Probabilités seminar, Universite d'Aix Marseilles,Luminy, France, 2013.03. |

25. | Fumio Hiroshima, Removal of UV cutoff of the Nelson model by stochastic analysis, 量子場の数理とその周辺, 2012.11. |

26. | Fumio Hiroshima, Spectral analysis of QFT by functional integrals with jump processes, SPA,Osaka, 2010.09. |

27. | Fumio Hiroshima, Functional integrations in quantum field theory, The 24th Max Born symposium, Wroclaw Univ., 2008.09. |

28. | Fumio Hiroshima, Feynman-Kac formula, Mini-course on Feynman-Kac formulas and their applications, Wien University, WPI, 2006.03, [URL]. |

29. | Fumio Hiroshima, Spectral analysis of Schrodinger operators coupled to a quantum field, MSJ, Hokkaido univ., special lecture, 2004.09. |

30. | Fumio Hiroshima, Self-adjointness of the Pauli-Fierz model for arbitrary coupling constants, Relativistic quantum system and quantum electrodynamics, Mathematisches Forschungsinstitut Oberwolfach, 2001.08. |

31. | Fumio Hiroshima, Spectral analysis of atoms interacting with a quantized radiation field, math and phys summer school lecturer, Gakushuin univ., 2000.09. |

32. | Fumio Hiroshima, Ground states of a system interacting with a radiation field: existence, uniqueness and expression, UAB Mathematical Physics Congress 99, Alabama univ. USA, 1999.03. |

33. | Fumio Hiroshima, Analysis of the Pauli-Fierz model for arbitrary coupling constant, Workshop on Open Classical and Quantum Field Theory, Lille univ. ,France, 1999.06. |

**Awards**

- MSJ 2019 Analysis prize

Educational

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