Kyushu University Academic Staff Educational and Research Activities Database
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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