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Fumio Hiroshima Last modified date:2021.06.25

Graduate School
Undergraduate School

 Reseacher Profiling Tool Kyushu University Pure
Academic Degree
Doctor of science
Country of degree conferring institution (Overseas)
Yes Doctor
Field of Specialization
Total Priod of education and research career in the foreign country
Outline Activities
I am studying the spectral analysis of operators on an infinite dimensional space. Especially, from the mathematical standpoint, we investigate the quantum field theory on pseudo-Riemannian manifolds by using operator theory, micro-local analysis, theory of one-parameter semigroup, stochastic analysis, functional integral.

The Hamiltonian that appears in quantum field theory can be mathematically regarded as an unbounded self-adjoint operator on Hilbert space. The spectrum of the self-adjoint operator is analyzed nonperturbatively and abstractly. The Hamiltonian of quantum field theory has an eigenvalue embedded in a continuous spectrum when the coupling constant is zero. It has been found that unlike discrete eigenvalues, the analysis of embedded eigenvalues ​​is subtle, and is different from the behavior of discrete eigenvalues. Kato's regular theory exists in the perturbation theory of discrete eigenvalues, and very many things have been established. However, there is no general theory about our analysis of the perturbations of the eigenvalues.

The goal is to analyze the existence / absence of the Hamiltonian ground state and the degree of degeneracy, analysis of infrared divergence / ultraviolet divergence, spectral scattering theory, resonance, renormalization theory, Gibbs measure, etc. In recent years, we have also been studying CCR representation theory and lattice Schrodinger-operators.


Feynmann-Kac formula, Gibbs measure, renormalization, Boson-Fock space, Euclidean field, infinite-dimensional Ornstein-Uhlenbeck process, Levy process, subordinator, exponential decay, Gaussian decay, ultraviolet cut, infrared cut, ground state, self-adjoint operator, noncommutative Perron-Frobenius theorem, local convergence of measure, Kato potential, Bernstein function, Pauli-Fierz model, Nelson model, spin-boson model, non-commutative harmonic oscillator (NCHO), Rabi model, spectrum zeta function, time operator, CCR, weak Weyl relation, Laplacian on lattice, semi-classical analysis
Research Interests
  • 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
  • Semi-classical analysis of QFT
    keyword : Wigner measure, coherent state, Pauli-Fierz model, Maxwell equations
  • 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
  • Gibbs measure and localizations
    keyword : Gibbs measure, ground states, UV renormalization, exponential decay
  • Spectral zeta functions
    keyword : Rabi model, non-commutative harmonic oscillator
  • Time operators and CCR representations
    keyword : time operator, CCR
  • Schrodinger operator on lattice
    keyword : lattice, spectrum
Academic Activities
1. F.Hiroshima and J. Lorinczi, Feynman-Kac-Type Theorems and Gibbs Measures on Path Space, Applications in Rigorous Quantum Field Theory, Walter de Gruyter, 536pages, 2020.03.
2. J. Lorinczi, F.Hiroshima and V. Betz, Feynman-Kac-Type Theorems and Gibbs Measures on Path Space, Feynman-Kac-Type Formulae and Gibbs Measures, Walter de Gruyter, 567pages, 2020.03.
3. Fumio Hiroshima, Ground States of Quantum Field Models, Springer, 140pages, 2019.10.
4. J. Lorinczi,F.Hiroshima and V. 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.
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.
1. F.Hiroshima, T.Hidaka and I.Sasaki, Spectrum of semi-relativistic Pauli-Fierz Hamiltonian II, J. Spectral Theoryから出版予定, 2021.10.
2. F. Hiroshima, Z. Muminov and U. Kuljanov, Threshold of discrete Schroedinger operators with delta potentials on n-dimensional lattice, Linear and Multilinear Algebra, online, 2020.05.
3. F.Hiroshima and O.Matte, Ground states and their associated Gibbs measures in the renormalized nelson model, preprint, 2019.04.
4. F.Hiroshima, A.Arai, Ultra-weak time operators of Schroedinger operators, Ann. Henri Poincare, 18, 2995-3033, 2017.10.
5. F.Hiroshima, T.Ichinose, J.Lorinczi, Kato's inequality for magnetic relativistic Schroedinger operators, Publ RIMS Kyoto., 53, 79-117, 2016.10.
6. Fumio Hiroshima, Itaru Sasaki, Enhanced binding of an N-particle system interacting with a scalar field II. Relativistic version, Publ RIMS Kyoto, 51, 655-690, 2015.02.
7. Fumio Hiroshima, Masao Hirokawa, Lozsef Lorinczi, Spin-boson model through a Poisson-driven stochastic process, Math Z, 277, 1165-1198, 2014.04.
8. Fumio Hiroshima, Functional integral approach of semi-relativistic Pauli-Fierz models, Advances in Mathematics, 269, 784-840, 2014.04.
9. F.Hiroshima, M.Gubinelli, J.Lorinczi, Ultraviolet renormalization of the Nelson Hamiltonian through functional integration, J.Funct.Anal., 267, 3125-3153, 2014.04.
10. C. Gerard, F. Hiroshima, A. Panatti and A. Suzuki, Absence of ground state of the Nelson model with a variable mass, J. Funct. Anal., 262, 1, 273--299, 2012.01.
11. C. Gerard, F. Hiroshima, A. Panatti and A. Suzuki, Infrared problem for the Nelson model with variable coefficients, Communications in Mathematical Physics, 308, 2, 543--566, 2011.03.
12. F. Hiroshima and A. Suzuki, Physical State for nonrelativistic quantum electrodynamics, Ann. Henri Poincare, 10, 913-953, 2009.05.
13. Fumio Hiroshima and Itaru Sasaki, Enhanced binding of an $N$ particle system interacting with a scalar field I, Math. Z., 259, 657-680, 2008.04.
14. Fumio Hiroshima and Jozsef Lorinczi, Functional integral representations of nonrelativistic quantum electrodynamics with spin 1/2, J. Funct. Anal., 254, 2127--2185, 2008.03.
15. Fumio Hiroshima, Fiber Hamiltonians in nonrelativistic quantum electrodynamics, J. Funct. Anal., 252, 314-355, 2007.10.
16. Masao Hirokawa, Fumio Hiroshima and Herbert Spohn, Ground state for point particle interacting through a massless scalar Bose field, Adv. in Math., 191, 339-392, 2005.01.
17. Fumio Hiroshima, Multiplicity of ground states in quantum field models:applications of aymptotic fields, J. Funct. Anal., 10.1016/j.jfa.2005.03.004, 224, 2, 431-470, 224, 431-470, 2005.01.
18. Fumio Hiroshima and Herbert Spohn, Enhanced binding through coupling to a quantum field, Ann. Henri Poincare, 2, 1159-1187, 2001.01.
19. Fumio Hiroshima, Ground states and spectrum of quantum electrodynamics of non-relativistic particles, Trans. Amer. Math. Soc., 353, 4497-4528, 2001.01.
20. Fumio Hiroshima, Essential self-adjointness of translation-invariant quantum field models for arbitrary coupling constants, Commun. Math. Phys., 211, 585-613, 2000.01.
21. Asao Arai, Masao Hirokawa and Fumio Hiroshima, On the absence of eigenvectors of Hamiltonians in a class of massless quantum field models without infrared cutoff, J. Funct. Anal., 168, 470-497, 1999.01.
1. 廣島文生, Localization of the ground state of the Nelson model, Himeji conference on PDE, 2021.03.
2. Fumio Hiroshima, Localizations of bound states of a renormalized Hamiltonian, Scattering, microlocal analysis and renormalisation,Mittag-Leffler Institute, Stockholm, 2020.06.
3. Fumio Hiroshima, Semi-classical analysis and Wigner measure for non-relativistic QED, NAKAMURA60, Gakushuin univ. , 2020.01.
4. Fumio Hiroshima, Stochastic renormalization, MSJ, Nippon univ. , special lecture, 2019.09.
5. Fumio Hiroshima, Hierarchy of CCR representations, Aarhus university, seminar, Denmark, 2018.10.
6. 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.
7. Fumio Hiroshima, Ground state of renormalized Nelson model, Aarhus university, Math. Phys. seminar, Denmark, 2017.12.
8. Fumio Hiroshima, Schroedinger operators on lattice, Second Summer School: Various aspects of mathematical physics,St Petersburg,Russia, 2017.07, [URL].
9. Fumio Hiroshima, Feynman-Kac formula and its application to quantum physics, Mathematical Analysis of Interacting Quantum Systems, Rennes univ., France, 2017.03.
10. Fumio Hiroshima, Analysis of time operators, La Sapienza univ. Math. Phys. seminar, Rome, 2017.02.
11. Fumio Hiroshima, Time operator associated with Schroedinger operators, QUTIS, Bilbao, Spain, 2016.09.
12. Fumio Hiroshima, Threshold ground state of the semi-relativistic Pauli-Fierz Hamiltonian,Aarhus university, Aarhus univ. Seminar, Denmark, 2016.02.
13. Fumio Hiroshima, Stochastic analysis of quantum field theory, MSJ, Kyoto Ind. univ. , special lecture, 2015.09.
14. Fumio Hiroshima, Analysis of ground state of quantum field theory by Gibbs measures, International Congress of Mathematical Physics(ICMP) 2015,Chile, 2015.08.
15. 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.
16. Fumio Hiroshima, Functional integral approach to mathematically rigorous quantum field theory, TJASSST2013, Tunisia, 2013.11.
17. Fumio Hiroshima, Gibbs measure approach to spin-boson model, International conference on stochastic analysis and applications, Tunisia, 2013.10.
18. Fumio Hiroshima, Non-relativistic QFT and Gibbs measures, math and phys summer school lecturer, Univ. Tokyo, 2013.09.
19. Fumio Hiroshima, Spectrum of non-commutative harmonic oscillator and related models, Bologna univ. seminar, Italy, 2013.09.
20. Fumio Hiroshima, Enhanced binding for quantum field models, Universite de Rennes 1 seminar, France, 2013.03.
21. 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.
22. 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.
23. Fumio Hiroshima, Spectral analysis of QFT by functional integrals with jump processes, SPA,Osaka, 2010.09.
24. Fumio Hiroshima, Functional integrations in quantum field theory, The 24th Max Born symposium, Wroclaw Univ., 2008.09.
25. Fumio Hiroshima, Feynman-Kac formula, Mini-course on Feynman-Kac formulas and their applications, Wien University, WPI, 2006.03, [URL].
26. Fumio Hiroshima, Spectral analysis of Schrodinger operators coupled to a quantum field, MSJ, Hokkaido univ., special lecture, 2004.09.
27. Fumio Hiroshima, Self-adjointness of the Pauli-Fierz model for arbitrary coupling constants, Relativistic quantum system and quantum electrodynamics, Mathematisches Forschungsinstitut Oberwolfach, 2001.08.
28. Fumio Hiroshima, Spectral analysis of atoms interacting with a quantized radiation field, math and phys summer school lecturer, Gakushuin univ., 2000.09.
29. 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.
30. 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.
  • MSJ 2019 Analysis prize
Educational Activities