1. F.Hiroshima and T. Shirai, Fiber decomposition of non-commutative harmonic oscillators by two-photon quantum Rabi models, [arXiv] 2024
2. F.Hiroshima and T. Shirai, Spectral zeta function and ground state of quantum Rabi model, [arXiv] 2024
3. F.Hiroshima and O.Matte, Point-wise spatial decay of eigenvectors in the Nelson model, in preparation.
4. B.Hinrichs and F.Hiroshima, On the ergodicity of renormalized translation invariant Nelson-type semigroups.
5. F.Hiroshima and N.Teranishi, Conjugate operators of 1D harmonic oscillator, [arXiv] 2024
6. F.Hiroshima and N.Teranishi, Self-adjointness of unbounded time operators, [arXiv] 2024
7. Sh. U. Alladustov, F.Hiroshima and M. I. Muminov, On the spectrum of discrete Schroedinger operator of a rank-two perturbation on Z, in preparation.
8. F.Hiroshima, Essential self-adjointness of Hamiltonians with singular potential in QFT, in preparation.
9. F. Hiroshima, Translation invariant models in QFT without ultraviolet cutoffs, [arXiv] 2015.
10. F. Hiroshima, Note on ultraviolet renormalization and ground state energy of the Nelson model, [arXiv] 2015.
71. F.Hiroshima and N.Teranishi, Time operators of harmonic oscillator and its representations, [arXiv], [J. Math. Phys. 65, 042105(2024)]
70. Z.Ammari, M.Falconi and F.Hiroshima, From the quantum to the classical electrodynamics of charges and fields, [arXiv] to be published in Annales de l'institut Fourier.
69. F.Hiroshima, Representations of Pauli-Fierz type models by path measures, Proceedings of the workshop "Mathematical Physics and its Interactions" [pdf]
68. F. Hiroshima, Z. Muminov and U. Kuljanov, Threshold of discrete Schroedinger operators with delta potentials on n-dimensional lattice, [pdf] [Linear and Multilinear Algebra 70 (2022) 919-954]
67. F.Hiroshima and O.Matte, Ground states and their associated Gibbs measures in the renormalized nelson model, [Rev. Math.Phys. (2022) online] [pdf]
66. T. Hidaka,F. Hiroshima and I.Sasaki, Spectrum of semi-relativistic Pauli-Fierz Hamiltonian II, [J. Spectral Theory 11 (2021) 1779-1830] [pdf]
65. S. Gheryani, F.Hiroshima, J.Lorinczi, A.Majid and H.Ouerdiane, Functional central limit theorem and P(phi)_1-process in quantum field theory, Mathematical Physics, Analysis and Geometry 23 online (2020),30pages. Lemma4とLemma8はエラー. 改訂版はこちら→[pdf]
64. F.Hiroshima, Point-wise exponential decay of bound states of the Nelson model with Kato-class potentials, ANALYSIS AND OPERATOR THEORY - In Honor of Tosio Kato's 100 th Birthday, Springer, 225-250, 2019.
63. A. Arai and F. Hiroshima, Ultra-weak time operators of Schroedinger operators, Ann. Henri Poincare 18,(2017),2995-3033.
62. F. Hiroshima,S.Osawa, Mass renormalization in the Nelson model, Int.J.Math and Math.Sci.Volume 2017 (2017), Article ID 4760105, 21 pages.
61. F. Hiroshima,T.Ichinose and J.Lorinczi, Kato's inequality for magnetic relativistic Schroedinger operators,Publ RIMS Kyoto 53,(2017),79-117.
60. T. Hidaka and F. Hiroshima, Spectrum of semi-relativistic Pauli-Fierz Hamiltonian I, J.Math.Anal.Appl.437,(2016),330-349.
59. F. Hiroshima and I. Sasaki, Enhanced binding of an N particle system interacting with a scalar field II, Relativistic version Publ RIMS Kyoto 51 (2015),655-690.
58. T. Hidaka and F. Hiroshima, Self-adjointness of semi-relativistic Pauli-Fierz models, Rev.Math.Phys.27 (2015) 1550015 18 pages.
57. F. Hiroshima, J. Lorinczi and U Rozikov, Periodic solutions of generalized Schroedinger equations on Cayley trees,Commun. Stochastic Analysis 9 (2015),283-296.
56. M. Hirokawa and F. Hiroshima, Absence of energy level crossing for the ground state energy of the Rabi model, Commun. Stochastic Analysis 8 (2014),551-560.
55. M. Gubinelli, F. Hiroshima and J. Lorinczi, Ultraviolet renormalization of the Nelson Hamiltonian through functional integration, [pdf] J.Funct.Anal. 267(2014),3125-3153.
54. F. Hiroshima, Functional integral approach to semi-relativistic Pauli-Fierz models, Adv. in Math. 259 (2014), 784-840.
53. M. Hirokawa, F. Hiroshima and J. Lorinczi, Spin-boson model through a Poisson-driven stochastic process, Math. Zeitschrift 277 (2014),1165-1198.
52. F. Hiroshima and J. Lorinczi, The Spectrum of non-local discrete Schroedinger operators with a delta-potential, Pacific J. Math-for-Industry 6 (2014), 6pages [pdf] [revised version (Table 3 and related parts are revised)]
51. F. Hiroshima and I. Sasaki, Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing, J. Math. Anal. Appl. 45 (2014), 595-609.
50. F. Hiroshima, T. Ichinose and J. Lorinczi, Probabilistic representation and fall-off of bound states of relativistic Schroedinger operators with spin 1/2, Publ RIMS Kyoto 49 (2013), 189-214.
49. F. Hiroshima and I. Sasaki, Multiplicity of the lowest eigenvalue of non-commutative harmonic oscillator, Kyushu J. Math. 67 (2013),355-366.
48. F. Hiroshima and J. Lorinczi, Lieb-Thirring bound for Schroedinger operators with Bernstein functions of the Laplacian, Commun. Stochastic Analysis 6 (2012), 589-602.
47. F. Hiroshima, I. Sasaki, T. Shirai and A. Suzuki, Note on the spectrum of discrete Schroedinger operators, J. Math-for-Industry 4 (2012), 105-108.
46. F. Hiroshima, J. Lorinczi and T. Takaesu, A probabilistic representation of the ground state expectation of fractional powers of the boson number operator, J. Math. Anal. Appl, 395 (2012), 437-447.
45. F. Hiroshima, T. Ichinose and J. Lorinczi, Path integral representation for Schroedinger operators with Bernstein functions of the Laplacian, Rev. Math. Phys. 24 (2012) 1250013 (40 pages).
44. C. Gerard, F. Hiroshima, A. Panati and A. Suzuki, Removal of the UV cutoff for the Nelson model with variable coefficients, Lett Math Phys, 101(2012), 305-322.
43. C. Gerard, F. Hiroshima, A. Panati and A. Suzuki, Absence of ground state of the Nelson model with variable coefficients, J. Funct. Anal. 262 (2012), 273-299.
42. C. Gerard, F. Hiroshima, A. Panati and A. Suzuki, Infrared problem for the Nelson model with variable coefficients, Commun. Math. Phys. 308 (2011), 543-566.
41. F. Hiroshima, H. Spohn and A. Suzuki, The no-binding regime of the Pauli-Fierz model, J. Math. Phys. 52, 062104 (2011).
40. F. Hiroshima and I. Sasaki, On the ionization energy of semi-relativistic Pauli-Fierz model for a single particle, RIMS Kokyuroku Bessatsu B21 (2010), 25-34.
39. C. Gerard, F. Hiroshima, A. Panati and A. Suzuki, Existence and absence of ground states for a particle interacting through the quantized scalar field on a static space-time, RIMS Kokyuroku Bessatsu B21 (2010), 15-24.
38. T. Hidaka and F. Hiroshima, Pauli-Fierz model with Kato-class potentials and exponential decays, Rev. Math. Phys. 22 (2010), 1181-1208.
37. F. Hiroshima, S. Kuribayashi and I. Sasaki, Self-adjoint extensions of momentum operators: application of weak Weyl relations, J. Math-for-Industry 2 (2010), 21-25.
36. F. Hiroshima and A. Suzuki, Physical state of nonrelativistic quantum electrodynamics, Ann. Henri Poincare 10 (2009), 913-953.
35. C. Gerard, F. Hiroshima, A. Panati and A. Suzuki, Infrared divergence of a scalar quantum field model on a pseudo Riemannian manifold, Interdisciplinary Information Science 15 (2009), 399-422.
34. V. Betz and F. Hiroshima, Gibbs measures with double stochastic integrals on path space, Infinite Dimensional Analysis, Quantum Probability and Related Topics 12 (2009), 135-152.
33. F. Hiroshima, S. Kuribayashi and Y. Matsuzawa, Strong time operator associated with generalized Hamiltonians, Lett. Math. Phys. 87 (2009), 115-123.
32. F. Hiroshima, Perturbation of embedded eigenvalues in quantum field theory, Sugaku exposition 21 (2008), 177-207.
31. F. Hiroshima and I. Sasaki, Enhanced binding of an N particle system interacting with a scalar field I, Math. Zeitschrift 259 (2008), 657-680.
30. F. Hiroshima and J. Lorinczi, Functional integral representations of the Pauli-Fierz model with spin 1/2, J. Funct. Anal. 254 (2008), 2127-2185.
29. F. Hiroshima, Fiber Hamiltonians in nonrelativistic quantum electrodynamics, J. Funct. Anal. 252 (2007), 314-355.
28. A. Arai, M. Hirokawa and F. Hiroshima, Regularities of ground states in quantum field models, Kyushu J. Math. 61 (2007), 321-372.
27. F. Hiroshima and K. T. Ito, Mass renormalization in nonrelativistic quantum electrodynamics with spin 1/2, Rev. Math. Phys. 19 (2007), 405-454.
26. F. Hiroshima, Multiplicity of ground states in quantum field models:applications of asymptotic fields, J. Funct. Anal. 224 (2005), 431-470.
25. F. Hiroshima and H. Spohn, Mass renormalization in nonrelativistic QED, J. Math. Phys. 46, 042302 (2005) (27pages).
24. M. Hirokawa, F. Hiroshima and H. Spohn, Ground state for point particle interacting through a massless scalar Bose field, Adv. in Math. 191 (2005), 339-392.
23. F. Hiroshima and K. R. Ito, Local exponent and infinitesimal generators of proper canonical transformations on a Boson Fock space, Infinite Dimensional Analysis, Quantum Probability and Related Topics 7 (2004), 547-572.
22. F. Hiroshima, Analysis of ground states of atoms interacting with a quantized radiation field, Topics in the theory of Schroedinger operators ed. H. Araki and H. Ezawa, 145-272, World Scientific, 2004.
21. F. Hiroshima, Nonrelativistic QED at large momentum of photons, Garden of Quanta eds. A. Tonomura et. al., 167-196, World Scientific, 2003.
20. F. Hiroshima, Localization of the number of photons of nonrelativistic QED, Rev. Math. Phys. 15 (2003), 271-312.
19. F. Hiroshima, Self-adjointness of the Pauli-Fierz Hamiltonian for arbitrary values of coupling constants, Ann. Henri Poincare 3 (2002), 171-201.
18. F. Hiroshima, Observable effect and parametrized scaling limits of a model in nonrelativistic quantum electrodynamics, J. Math. Phys. 43 (2002), 1755-1795.
17. V. Betz, F. Hiroshima, J. Lorinczi, R. Minlos and H. Spohn, Ground state properties of the Nelson Hamiltonian-A Gibbs measure-based approach, Rev. Math. Phys. 14 (2002), 173-198.
16. F. Hiroshima, Embedded eigenvalues, localization and asymptotics of quantum field models: a functional integral approach, J. Phys. A: Math. Gen. 35 (2002), 351-375.
15. F. Hiroshima and H. Spohn, Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin, Adv. Theor. Math. Phys. 5 (2001), 1091-1104.
14. F. Hiroshima and H. Spohn, Enhanced binding through coupling to a quantum field, Ann. Henri Poincare 2 (2001), 1159-1187.
13. F. Hiroshima, Ground states and spectrum of quantum electrodynamics of non-relativistic particles, Trans. Amer. Math. Soc. 353 (2001), 4497-4528.
12. F. Hiroshima, Essential self-adjointness of translation-invariant quantum field models for arbitrary coupling constants, Commun. Math. Phys. 211 (2000), 585-613.
11. F. Hiroshima, Euclidean Gell-Mann-Low formula and double stochastic integrals, Stochastic Processes, Physics and Geometry: New Interplays. II, Canadian Mathematical Society, conference proceedings 29 (2000), 285-292.
10. F. Hiroshima, Ground states of a model in nonrelativistic quantum electrodynamics II, J. Math. Phys. 41 (2000), 661-674.
9. F. Hiroshima, Ground states of a model in nonrelativistic quantum electrodynamics I, J. Math. Phys. 40 (1999), 6209-6222.
8. A. Arai, M. Hirokawa and F. Hiroshima, On the absence of eigenvectors of Hamiltonians in a class of massless quantum field models without infrared cutoff, J. Funct. Anal. 168 (1999), 470-497.
7. F. Hiroshima, Weak coupling limit removing an ultraviolet cut-off for a Hamiltonian of particles interacting with a quantized scalar field, J. Math. Phys. 40 (1999), 1215-1236.
6. F. Hiroshima, Weak coupling limit and a removal of an ultraviolet cut-off for a Hamiltonian of particles interacting with a massive scalar field, Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 (1998), 407-423.
5. F. Hiroshima, Asymptotic behaviors of an interaction Hamiltonian, Nonlinear Analysis, Theory, Methods and Application 30 (1997), 4863-4874.
4. F. Hiroshima, Functional integral representation of a model in quantum electrodynamics, Rev. Math. Phys. 9 (1997), 489-530.
3. F. Hiroshima, A scaling limit of a Hamiltonian of many nonrelativistic particles interacting with a quantized radiation field, Rev. Math. Phys. 9 (1997), 201-225.
2. F. Hiroshima, Diamagnetic inequalities for systems of nonrelativistic particles with a quantized field, Rev. Math. Phys. 8 (1996), 185-203.
1. F. Hiroshima, Scaling limit of a model of quantum electrodynamics, J. Math. Phys. 34 (1993), 4478-4518.