Publications

Recent Publications

  1. Parametrization of degenerate density matrices. Reviews in Mathematical Physics Vol. 29 No. 8 (2017) 1750026-1 to 1750026-39 Review in Mathematical Physics; to gether with S. Nagamachi.
  2. Mathematical Methods in Physics - Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics. Second Edition. Series: Progress in Mathematical Physics, Vol. 69; Birkhäuser Boston New York  2015, 598 pages; together with Ph.Blanchard.
  3. Edge of the wedge theorem for tempered ultra-hyperfunctions. Complex Variables and Elliptic Equations. An International Journal, 2013 Complex Variables and Elliptic Equations; to gether with S. Nagamachi.
  4. Solution of a Linearized Model of Heisenberg’s Fundamental Equation. Chapter in book Advances in Quantum Field Theory, InTech, ed. S. Ketov, 2012; to gether with S. Nagamachi.
  5. TOPICAL REVIEW Parametrizations of density matrices. Journal of Modern Optics 2012, 1-20, Vol. 59, Issue 11; together with H. Mäkelä, A. Messina and F. Petruccione.
  6. Reply to ``Comment on `Remarks on the structure of states of composite quantum systems and envariance'[Phys. Lett. A 355 (2006)180]"[Phys. Lett. A 375 (2011) 1160]}. Phys. Lett. A 375 (2011) 1163-1165; together with Ph. Blanchard.
  7. Frame independence of the fundamental length in relativistic quantum field theory. Journal of Mathematical Physics 51, 022305 (2010); 18 pages, DOI: 10.1063/1.3276441; together with S. Nagamachi.
  8. Nonlinear mappings for density matrices. Physica E 42, Issue 3, (January 2010) 436-438; together with F. Petruccione.
  9. Parametrizing density matrices for composite systems. Open Systems & Information Dynamics Vol. 15, Issue 4 (December 2008), 397 - 408; together with D. Chruściński and F. Petruccione.
  10. Density matrices and their time evolution. Open Systems & Information Dynamics Vol. 15, Issue 2 (June 2008), 109 - 121; together with F. Petruccione.
  11. Quantum teleportation and holomorphic representation of CCR. Open Systems & Information Dynamics Vol. 15, No.1 (2008) 1-18; together with S. Nagamachi.
  12. Solution of a linearized model of Heisenberg's fundamental equation II. Journal of Mathematical Physics Vol. 49, 052304 (2008); together with S. Nagamachi.
  13. A note on localized directional weak lower semi-continuity; Questiones Mathematicae 29 (2006), 376--381.
  14. Remarks on the structure of states of composite quantum systems and envariance; Physics Letter A 355 (2006) 180--187;  together with Ph. Blanchard. 
  15. General formula for comparison of clock rates - applications to cosmos and solar system; Class. Quantum Grav. Vol. 22, November 2005, 5015--5028; together with Chongming Xu and Xuejun Wu.
  16. Relativistic quantum field theory with a fundamental length; Journal of Mathematical Physics Vol. 45, No. 6, June 2004, 2199 - 2231; together with S. Nagamachi.


Selected Publications
(before 2004)
  1. Hyperfunction quantum field theory: Analytic structure, modular aspects, and local observable algebras;Journ. of Math. Phys. Vol. 42, No. 1, January 2001, 1-31; together with S. Nagamachi.
  2. Closure of field operators, asymptotic {A}belianness, and vacuum structure in hyperfunction quantum field theory; Journ. of Math. Phys. Vol. 39, No. 10, October 1998,5098-5111; together with S. Nagamachi.
  3. Eigenvalue Problems for Global Quasilinear Partial Differential  Operators; Communications on Applied Nonlinear Analysis 4(1997), No. 3, 55-67.
  4. How to reconstruct an analytic function from its asymptotic expansion? Complex Variables - Theory and Application Vol. 29(1996), 1 - 22.
  5. Inflationary Cosmology with a $R + \lambda R_{\mu \nu} R^{\mu \nu}/R$ Lagrangian; General Relativity and Gravitation 26(12) (1994) 1197 - 1211; together with DH Coule and C Xu.
  6. Minimization without Weak Lower Semicontinuity; Applicable Analysis Vol. 54 (1994), 91 - 111.
  7. Uniqueness in Moment-Problems over Nuclear Spaces and Weak Convergence of Radon Probability Measures; Reviews of Mathematical Physics Vol. 5, No. 4 (1993) 631-658.
  8. On the Variational Approach to Semilinear Elliptic Equations with Scale-Covariance; Journ. Diff. Eq. 83, 109-144 (1990).
  9. Hyperfunction Quantum Field Theory - Basic Structural Results; Journ. Math. Phys. 30(10), 2340-2359 (1989); with S.
    Nagamachi.
  10. Invariance of Essential Spectra for Perturbations with Hard Cores; Lett. Math. Phys. 13, 69-77 (1987), with M. Demuth and F. Gesztesy.
  11. On Essential Spectra of Hard Core Type Schrödinger Operators; J. Phys. A.: Math. Gen. 18, L7 - L11 (1985), with F. Gesztesy.
  12. On the Construction of Fields and the Toplogical Role of Jacobi-Fields; Rep. Math. Phys. 21, 143-158 (1985).
  13. Continuity of Wave- and Scattering- Operators with Respect to Interactions; Journ. Math. Phys. 24, 1516-1528 (1983), with F. Gesztesy.
  14. The n-Field Irreducible Part of a n-Point Functional; Annal. de L'Institut Henri Poincaré, Sect. A., Vol. XXIV no. 3, 309-328 (1981).
  15. On the Characterization of Relativistic Quantum Field Theories in Terms of Finitely Many Vacuum Expectation Values II; Commun. Math. Phys. 58, 167-194 (1978).
  16. On the Characterization of Relativistic Quantum Field Theories in Terms of Finitely Many Vacuum Expectation Values I; Commun. Math. Phys. 58, 139-166 (1978).
  17. On the Equivalence of Scaling, Light-Cone Singularities, and the Asymptotic Behaviour of the Jost-Lehmann Spectral Function; Commun. Math. Phys. 36, 137-156 (1974); with P. Stichel.


Selection of Contributions to Conference Proceedings

  1. Localization in quantum field theory; pages 243 - 274, in: A Garden of Quanta - Essays in Honor of Hiroshi Ezawa; eds. J Arafune, A Arai, M Kobayashi et al., World Scientific New Jersey London Singapore Hong Kong 2003; together with S. Nagamachi.
  2. Non-convex minimization - the case of vector fields;  in: Partial Differential Equations and Spectral Theory, Proceedings of the International Conference PDE2000, Clausthal (Germany), 24 - 28 July 2000; eds. M. Demuth and B.-W. Schulze, Birkhäuser, Boston 2001; Series: Operator Theory.
  3. Some generalized Laplace transformations; in: Proceedings of 1997 Congress of ISAAC, University of Delaware, Newark (USA), 3-10 June 1997; Section "Reproducing Kernels and their Applications", eds. R. Gilbert, D. Martin, S. Saitoh, Kluwer Academic Publishers Dordrecht Boston London 1999.
  4. Extended Rees-Sciama Effect and anisotropic Microwave Background Radiation; in Proceedings of IAU Symp. 183 (1998): Cosmological Parameters and the Evolution of the Universe; with Xuejun Wu and Chongming Xu.
  5. On the role of symmetries in PDE-problems; II. International Wigner Symposium, Goslar, Germany, July 1991; in "Classical and Quantum Systems - Foundations and Symmetries, Proceedings, pp 734-737, editors: H.D. Doebner et al., World Scientific, Singapore 1993.
  6. A Note on Solutions of Two-Dimensional Semilinear Elliptic Vector-Field Equations with Strong Nonlinearity; in 'New Methods and Results in Nonlinear Field Equations', pp 37-52, editors: Ph. Blanchard et al., LNP 347, Springer-Verlag Berlin Heidelberg New York 1989.
  7. When is a Field a Jacobi-Field? A Characterization of States on Tensor Algebras; International Conference "Global Analysis and Mathematical Physics", Reinhardsbrunn/Friedrichroda, FRG, 1985; in: Rep. Akad. Wiss. DDR, Inst. Math., R-Math. 01/86(1986).
  8. An Analysis of some Non-linear Aspects of Quantum Field Theory; in "Mathematical Problems in Theoretical Physics", editors: R. Schrader, R. Seiler, D.A. Uhlenbrock, LNP 153,Springer-Verlag Berlin Heidelberg New York 1982.
    9.



Books

  1. Direkte Methoden der Variationsrechnung. Ein Lehrbuch. Springer-Verlag Wien 1982, 295 pages; together with Ph.Blanchard.
  2. Variational Methods in Mathematical Physics. A Unified Approach. Translated, revised, and extended edition of 1., Springer-Verlag Berlin Heidelberg New York 1992, 410 pages; together with Ph. Blanchard.
    3. Variational Methods Variational Methods
  3. Distributionen und Hilbert-Raum Operatoren. Mathematische Methoden der Physik. Springer-Verlag Wien New York October 1993, 374 pages; together with Ph. Blanchard.
  4. Mathematical Methods in Physics - Distributions, Hilbert Space Operators, and Variational Methods. Series: Progress in Mathematical Physics, Vol. 26; Birkhäuser Boston New York  2003, 471 pages; together with Ph.Blanchard.
    5. Mathematical Methods Mathematical Methods
  5. Mathematical Methods in Physics - Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics. Second Edition. Series: Progress in Mathematical Physics, Vol. 69; Birkhäuser Boston New York  2015, 598 pages; together with Ph.Blanchard.
    6. Mathematical Methods Mathematical Methods



Books (edited)

  1. Emerging Quantum Technologies. Selected Theoretical and Experimental Aspects. EPJ ST Special Topics Vol. 159. EDP Sciences, Springer 2008, 140 pages; together with Ph.Blanchard and F. Petruccione.
    2. EPJ EPJ
  2. Theoretical Foundations of Quantum Information Processing and Communication. Selected Topics. Lecture Notes in Physics Vol. 787. 253 pages; Springer 2010. together with F. Petruccione.
    3. TFQIPC-f TFQIPC-b

  3. Quantum Africa 2010: Theoretical and Experimental Foundations of Recent Quantum Technology. AIP Conference Proceedings 1469., 125 pages; American Institute of Physics 2012. together with T. Konrad and F. Petruccione.
    4. TFQIPC-f TFQIPC-b


    On request (if available) I will send copies of my papers and/or my complete list of publications.