Fumio Hiroshima | Last modified date：2016.10.27 |

Graduate School

Undergraduate School

Phone

092-802-4473

Academic Degree

Doctor of science

Field of Specialization

Analysis

Outline Activities

Hamiltonians in the quantum field theory on a static pseudo Riemanian manifold can be regarded as unbounded self-adjoint operators on Hilbert spaces. I analyse the spectrum of the Hamiltonian non-pertubatively. Perturbations of embedded eigenvalues in thye continuous spectrum, and UV and IR divergences are the subtle problems. The existence and absence of ground states, the multiplicity of ground states, spectral scattering theory, resonances and renormalizations are studied by using operator theory, functional integrals, microlocal analysis, the theory of one-parameter semi-groups and renormalization group.

Research

**Research Interests**

- Gibbs measure

keyword : Gibbs measure

2008.10～2017.03. - time operators

keyword : time operator, CCR

2010.10～2017.03. - Spectral analysis of Schroedinger operator on lattice

keyword : lattice, spectrum

2012.04～2015.11. - Spectral zeta function

keyword : Rabi model, non-commutative harmonic oscillator

2013.10～2014.10. - Spectral analysis of quantum field theory

keyword : quantum field theory, spectral analysis, Fock space, semigroup, embedded eigenvalues, ground states, scattering theory, pseudo Riemann manifold, resonances, renormalization group, functional inegrations, Gibbs measures, Feynman-Kac formulae, double potent

1998.10Hamiltonians in the quantum field theory can be regarded as self-adjoint operators on Hilbert spaces. I analyse the spectrum of the Hamiltonian non-pertubatively. Perturbations of embedded eigenvalues and ultraviolet and infrared divergences are the subtle problems. The existence and absence of ground states, the multiplicity of ground states, spectral scattering theory, resonances and renormalizations are studied by using operator theory, functional integrals, Gibbs measures, the theory of one-parameter semi-groups and renormalization group..

**Academic Activities**

**Books**

1. | Fumio Hiroshima, Ground States of Quantum Field Models, Springer, 出版予定, 2018.04. |

2. | Fumio Hiroshima, Jozsef Lorinczi, Volker Betz, Feynman-Kac-Type Theorems and Gibbs Measures on Path Space, Feynman-Kac-Type Formulae and Gibbs Measures, 2nd Edition, Volume 1, 2, Walter de Gruyter, 出版予定, 2017.10. |

3. | Fumio Hiroshima, Jozsef Lorinczi, Volker Betz, Feynman-Kac type theorems and Gibbs measures on path space. With applications into rigorous quantum field theory, Walter de Gruyter, Studies in Mathematics 34 , 2011.09. |

**Reports**

1. | Fumio Hiroshima, Itaru Sasaki, Herbert Spohn and Akito Suzuki, Enhanced binding in quantum field theory, COE Lecture Note 38 (Math-for-Industry), 2012.02. |

2. | Perturbation problems of embedded eigenvalues in quantum field theory. |

**Papers**

1. | Fumio Hiroshima, Functional integral approach of semi-relativistic Pauli-Fierz models, Advances in Mathematics, 269, 2014.04. |

2. | F.Hiroshima, M.Gubinelli, J.Lorinczi, Ultraviolet renormalization of the Nelson Hamiltonian through functional integration,, J.Funct.Anal., 267, 2014.04. |

**Presentations**

1. | 廣島 文生, Time operator associated with Schroedinger operators, QUTIS, 2016.09. |

2. | 廣島 文生, Analysis of ground state of quantum field theory by Gibbs measures, International Congress of Mathematical Physics(ICMP) 2015, 2015.08.01. |

3. | 廣島 文生, Spectrum of semi-relativistic QED by a Gibbs measure, The 51 winter school of theoretical physics(Karpacz Winter Schools in Theoretical Physics), 2015.02.11. |

4. | Fumio Hiroshima, Functional integral approach to mathematically rigorous quantum field theory, TJASSST2013, 2013.11.15. |

5. | Fumio Hiroshima, Gibbs measure approach to spin-boson model , International conference on stochastic analysis and applications, 2013.10.17. |

6. | , [URL]. |

7. | Spectral analysis of Schrodinger operators coupled to a qunatm field. |

Educational

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