1. |
F.Hiroshima, T.Hidaka, I.Sasaki, Spectrum of semi-relativistic Pauli-Fierz Hamiltonian II, *preprint*, 2016.10. |

2. |
F.Hiroshima, A.Arai, Ultra-weak time operators of Schroedinger operators, *preprint*, 2016.10, In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f:ℝ→ℝ such that f(HV) has an ultra-weak time operator is found.. |

3. |
F.Hiroshima, T.Ichinose, J.Lorinczi, Kato's inequality for magnetic relativistic Schroedinger operators, *to appear in Publ RIMS Kyoto.*, 2016.10. |

4. |
Fumio Hiroshima, Takeru Hidaka, Spectrum of the semi-relativistic Pauli-Fierz model I, *J.Math.Anal.Appl.*, 437, 330-349, 2016.04, Relativistic PF model is studied in the non-perturbative way.. |

5. |
Fumio Hiroshima, Takeru Hidaka, Self-adjointness of semi-relativistic Pauli-Fierz Hamiltonian, *Rev.Math.Phys.*, 27, 1550015,18page, 2015.04. |

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, Absence of energy level crossing for the ground state energy of the Rabi model, * Communications in Stochastic Analysis*, 9, 551-560, 2014.07. |

8. |
Fumio Hiroshima, Jozsef Lorinczi, The Spectrum of non-local discrete Schroedinger operators with a delta-potential, *Pacific J. Math-for-Industry *, 6, 6pages, 2014.04, Pacific J. Math-for-Industry 6 (2014), 6pages [pdf]. |

9. |
Fumio Hiroshima, Itaru Sasaki, Spectral analysis of non-commutative harmonic oscillators:the lowest eigenvalue and no crossing, *J. Math. Anal and Apple.*, 45, 595-609, 2014.04. |

10. |
Fumio Hiroshima, Masao Hirokawa, Lozsef Lorinczi, Spin-boson model through a Poisson-driven stochastic process, *Math Z*, 277, 1165-1198, 2014.04. |

11. |
Fumio Hiroshima, Functional integral approach of semi-relativistic Pauli-Fierz models, *Advances in Mathematics*, 269, 784-840, 2014.04. |

12. |
F.Hiroshima, M.Gubinelli, J.Lorinczi, Ultraviolet renormalization of the Nelson Hamiltonian through functional integration,, *J.Funct.Anal.*, 267, 3125-3153, 2014.04. |

13. |
Fumio Hiroshima and Itaru Sasaki, Multiplicity of the lowest eigenvalues of non-commutative harmonic oscillators, * Kyushu J. Math *, 67, 355-366, 2013.01. |

14. |
F. Hiroshima, T. Ichinose and J. Lorinczi, Probabilistic representation and fall-off of bound states of relativistic Schrodinger operators with spin 1/2, *Publ RIMS Kyoto*, 49, 189-214, 2013.01. |

15. |
Fumio Hiroshima, Itaru Sasaki, Tomoyuki Shirai and Akito Suzuki, Note on the spectrum of discrete Schroedinger operators, *Journal of Math for Industry*, 4, 105-108, 2012.10. |

16. |
Fumio Hiroshima and Jozsef Lorinczi, Lieb-Thirring bound for Schroedinger operators with Bernstein function of the Laplacian, *Commun. on Stochastic Anal.*, 6, 589-602, 2012.10. |

17. |
Fumio Hiroshima, Itaru Sasaki, Herbert Spohn and Akito Suzuki , Enhanced binding in quantum field theory , *COE Lecture Note (Kyushu University)*, 38, 206ページ, 2012.03. |

18. |
C. Gerard, F. Hiroshima, A. Panatti and A. Suzuki, Removal of the UV cutoff for the Nelson model with variable coefficients, *Lett Math Phys*, 101, 305--322, 2012.03. |

19. |
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. |

20. |
V.Betz, F.Hiroshima and J. Lorinczi, Feynman-Kac-Type Theorems and Gibbs Measures on Path Space. With Applications into Rigorous Quantum Field Theory, *de Gruyter Studies in Mathematics *, 507ページ, 34, 2011.07. |

21. |
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. |

22. |
Fumio Hiroshima, Herbert Spohn and Akito Suzuki, The no-enhanced regime of the Pauli-Fierz model, *J. Math. Phys. *, 52 , 062104 , 2011.02. |

23. |
Fumio Hiroshima and Itaru Sasaki, On the ionaization energy of semi-relativistic Pauli-Fierz model for a single particle, *RIMS Kokyuroku Bessatsu*, 21, 25-34, 2010.12. |

24. |
C. Gerard, F. Hiroshima, A. Panatti and A. Suzuki, Existence and absence of ground states for a particle interacting through the quantized scalar field on a static spacetime, *RIMS Kokyuroku Bessatsu*, 21, 15-24, 2010.12. |

25. |
Takeru Hidaka and Fumio Hiroshima , Pauli-Fierz model with Kato-class potentials and exponetial decays, *Rev. Math. Phys. *, 22, 1181-1208, 2010.04. |

26. |
Fumio Hiroshima, Sotaro Kuribayashi and Itaru Sasaki, Self-adjoint extensions of momentum operators:application of weak Weyl relations, *J. Math-for-Industry*, to appear , 2010.04. |

27. |
F. Hiroshima and A. Suzuki, Physical State for nonrelativistic quantum electrodynamics, *Ann. Henri Poincare*, 10, 913-953, 2009.05. |

28. |
F. Hiroshima, T. Ichinose and J. Lorinczi, Path integral representation for generalized Schrodinger operators with Bernstein function of the Laplacian, *Rev Math Phys*, 24, 1250013(40pages), 2009.03. |

29. |
C. Gerard, F. Hiroshima, A. Panatti and A. Suzuki, Infrared divergence of a scalar quantum field model on a pseudo Riemannian manifold., *Interdisplinary Information Science *, 15, 399-422, 2009.03. |

30. |
Fumio Hiroshima and Volker Betz, Gibbs measures with double stochastic integrals on path space , * Infinite Dimensional Analysis and Quantum Probability.*, 12, 135-152, 2009.03. |

31. |
Fumio Hiroshima, Yasumichi Matsuzawa, Sotaro Kuribayashi, Strong time operators associated with generalized Hamiltonians, *Lett Math Phys*, 87, 115-123. , 2009.01. |

32. |
Fumio Hiroshima, Perturbation of embedded eigenvalues in quantum field theory, *Sugaku Exp.*, 21, 177-207., 2008.12. |

33. |
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. |

34. |
Fumio Hiroshima and Jozsef Lorinczi, Functional integral representations of nonrelativistic quantum electrodynamics with spin 1/2 , *J. Funct. Anal. *, 254, 2127--2185, 2008.03. |

35. |
Fumio Hiroshima, Fiber Hamiltonians in nonrelativistic quantum electrodynamics, *J. Funct. Anal. *, 252, 314-355, 2007.10. |

36. |
Asao Arai, Masao Hirokawa and Fumio Hiroshima, Regularites of ground states of quantum field models , *Kyushu J. Math. *, 61, 321--372, 2007.10. |

37. |
Fumio Hiroshima and KR Ito, Mass renormalization in non-relativistic QED with spin 1/2, *Rev. Math. Phys.*, 19, 405-454, 2007.05. |

38. |
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. |

39. |
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. |

40. |
Fumio Hiroshima and Herbert Spohn, Mass renormalization in nonrelativistic QED, *J. Math. Phys.*, 46, 042302, 2005.01. |

41. |
Fumio Hiroshima and K.R. Ito, Local exponent and infinitesimal generators of proper canonical transformations on a Boson Fock space, *Infinite Dimensional Analysis, Quantum Probaility and Related Topics*, 7, 547-572, 2004.10. |

42. |
Fumio Hiroshima, Analysis of ground states of atoms interacting with a quantized radiation field, *Topics in the theory of Schrodinger operators
*, 145-272, 2004.01. |

43. |
Fumio Hiroshima, Localization of the number of photons of nonrelativistic QED, *Rev. Math. Phys.*, 15, 271-312, 2003.01. |

44. |
Fumio Hiroshima, Nonrelativistic QED at large momentum of photons, *Garden of Quanta*, 167-196, 2003.01. |

45. |
Fumio Hiroshima, Embedded eigenvalues, localization and asymptotics of quantum field models: a functional integral approach, *J. Phys. A: Math. Gen.*, 35, 351-375, 2002.04. |

46. |
Fumio Hiroshima, Observable effect and parametrized scaling limits of a model in nonrelativistic quantum electrodynamics, *J. Math. Phys.*, 43, 1755-1795, 2002.01. |

47. |
Fumio Hiroshima, Self-adjointness of the Pauli-Fierz Hamiltonian for arbitrary values of coupling constants, *Ann. Henri Poincare*, 3, 171-201, 2002.01. |

48. |
Volker Betz, Fumio Hiroshima, Jozsef Lorinczi Herbert Spohn and Robert Minlos, Ground state properties of the Nelson Hamiltonian-A Gibbs measure-based approach, *Rev. Math. Phys.*, 14, 173-198, 2002.01. |

49. |
Fumio Hiroshima and Herbert Spohn, Enhanced binding through coupling to a quantum field, *Ann. Henri Poincare*, 2, 1159-1187, 2001.01. |

50. |
Fumio Hiroshima, Ground states and spectrum of quantum electrodynamics of non-relativistic particles, *Trans. Amer. Math. Soc. *, 353, 4497-4528, 2001.01. |

51. |
Fumio Hiroshima and Herbert Spohn, Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin, *Adcvances in Theoretical and hematical Physics*, 5, 1091-1104, 2001.01. |

52. |
Fumio Hiroshima, Euclidean Gell-Mann-Low formula and double stochastic integrals, *Canadaian Math. Soc., Stochastic Processes, Physics and Geometry: New Interplays*, 29, 285-292, 2000.10. |

53. |
Fumio Hiroshima, Essential self-adjointness of translation-invariant quantum field models for arbitrary coupling constants, *Commun. Math. Phys.*, 211, 585-613, 2000.01. |

54. |
Fumio Hiroshima, Ground states of a model in nonrelativistic quantum electrodynamics II, *J. Math. Phys.*, 41, 661-674, 2000.01. |

55. |
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. |

56. |
Fumio Hiroshima, Weak coupling limit removing an ultraviolet cut-off for a Hamiltonian of particles interacting with a quantized scalar field, *J. Math. Phys.*, 40,1215-1236, 1999.01. |

57. |
Fumio Hiroshima, Ground states of a model in nonrelativistic quantum electrodynamics I, *J. Math. Phys*, 40, 6209-6222, 1999.01. |

58. |
Fumio Hiroshima , Weak coupling limit and a removal of an ultraviolet cutoff and a Hamiltonian of particles interacting with a massive scalar field, *Inf. Dim. Anal. and Quntum Prob. Relat. Top.*, 1, 407--423, 1998.09. |

59. |
Fumio Hiroshima, Functional integral representation of a model in quantum electrodynamics, *Rev. Math. Phys.*, 9, 489--530, 1997.09. |

60. |
Fumio Hiroshima , Asymptotic behaviors of an interaction Hamiltonian, *Nonlinear Analysis*, 30, 4863--4874, 1997.09. |

61. |
Fumio Hiroshima , Scaling limit of a model of quantum electrodynamics with many nonrelativistic particles, *Rev. Math. Phys.*, 9, 201--225, 1997.09. |

62. |
Fumio Hiroshima, Diamagnetic inequalities for systems of nonrelativistic particles with a quantized field, *Rev. Math. Phys.*, 8, 185--203, 1996.09. |

63. |
Fumio Hiroshima , Scaling limit of a model in quantum electrodynamics, *J. Math. Phys.*, 34, 4478--4518, 1993.09. |