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Fumio Hiroshima Last modified date：2024.04.04

Professor / Division of Analysis
Faculty of Mathematics


Graduate School
Joint Graduate School of Mathematics for Innovation
Department of Mathematics
Graduate School of Mathematics
Undergraduate School
Department of Mathematics
School of Sciences


Homepage
https://kyushu-u.elsevierpure.com/en/persons/fumio-hiroshima
　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.
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
 Show All Books >>
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.
Reports
 Show All 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
 Show All Papers >>
1. F.Hiroshima and O.Matte, Ground states and their associated Gibbs measures in the renormalized nelson model, Rev. Math.Phys., https://doi.org/10.1142/S0129055X22500027, ３４, 2, 84ページ, 2022.04.
2. F.Hiroshima, T.Hidaka and I.Sasaki, Spectrum of semi-relativistic Pauli-Fierz Hamiltonian II, J. Spectral Theory, DOI 10.4171/JST/386, １１, 1179-1830, 2021.10.
3. F. Hiroshima, Z. Muminov and U. Kuljanov, Threshold of discrete Schroedinger operators with delta potentials on n-dimensional lattice, Linear and Multilinear Algebra, online, 2022.05.
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.
Presentations
 Show All 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
Educational Activities
　


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