**Prof. Dr. Ismail Hakki DURU**

**Address:**

Izmir Institute of Technology

Faculty of Science

Department of Mathematics

TR35430

Urla / Izmir

TURKEY

**Tel :**
0 232 750 75 04

**Fax : **0 232 750 75 09

**e-mail : **ihduru@galois.iyte.edu.tr

**Curriculum Vitae**

Date of Birth :December 6 1946, Bolu

B.S. :Physics, University of Ankara, Faculty of Science, 1968

Ph.D. :Theoretical High Energy Physics, University of Colorado, USA, 1972

**Academic Positions:**

Teaching Assistant : University of Ankara, Faculty of Science, 1973- 1977

Associate Professor : University of Ankara, Faculty of Science, 1977- 1981

Dicle University, Faculty of Science, 1981-1983

TÜBITAK Senior Scientist: TUBITAK, Research Institute for Basic Sciences, 1984-1990

Professor: Trakya University, Department of Mathematics, 1990-2002

Senior Scientist at Feza Gürsey Institute on a part time consultant, 1990-2002

Senior Scientist at Feza Gürsey Institute on a full time consultant, 2002- 2005

Professor: Izmir Institute of Technology, Department of Mathematics, 2006-Member of

Academy of Sciences of Turkey (TUBA): 1994-November 2011

Member ofScience Academy Society: November 2011-

**Administrative Positions:**

Chairman :Department of Mathematics, Trakya University; 1992-2001Dean :Faculty of Arts and Science, Trakya University; 1997-2000

Director :Feza Gürsey Institute; 2000-2005

Dean :Faculty of Arts and Science, Izmir Institute of Technology; 2006-November 2010

**Research Topics:**

Dynamical groups, infinite dimensional field equations, path integrals in Quantum Mechanics, quantum field theory and condensed matter physics, vacuum structure in cosmology and media with electromagnetic fields,particle production, Interrelation between quantum fields and geometry, Aharonov-Bohm and Casimir effects, q-deformation and quantum groups.

**Courses taught:**

In Physics Department: Introductory physics, (Berkeley series), Statistical Physics, Electrodynamics, Quantum Mechanics, Quantum Field Theory, Atomic Physics.

In Mathematics Department: Real Analysis, Complex Analysis, Partial Differential Equations, Theory Group Representations, Topological Manifolds, p-adic numbers.

**Scholarships:**

NATO scholarship during B.S. studies 1964-1968

NATO Ph.D scholarship at USA, 1968-1972

Alexander von Humboldt scholarship, Berlin, 1978-1980

Trieste, International Center for Theoretical Physics "Associate Member", 1996-2001.

**Art Exhibitions :**

Arsiv Sanat Galerisi, Istanbul, October 1991.

Turco-British Association, Ankara, January 1992.

Devlet Güzel Sanatlar Galerisi, Edirne, January 1993.

Arsiv Sanat Galerisi, Istanbul, March 1994.

Turco-British Association, Ankara, January 1995.

Arsiv Sanat Galerisi, Istanbul, November 1996

**Publications:**

1) Introduction of Internal Coordinates into the Infinite-Component Majorana Equation, Proc.R.Soc.London, A 333, 217-224 (1973) (with A.O.Barut).2) On Relativistic Models with Multiplet Structures, Lett.Nuovo Cimento, 8, 768-770 (1973) (with A.O.Barut).

3) Relativistic Composite Systems and Minimal Coupling, Phys.Rev. D-10, 3448-3454 (1974) (with A.O.Barut).

4) Internal Structure of Composite Systems Described by Infinite-Component Wave Equations; Phys.Rev. D-15, 2401-2404 (1977)

5) Solution of the Path Integral for the H-Atom, Phys.Lett. 84 B, 185-188 (1979) (with H.Kleinert).

6) Hamilton-Jacobi Formulation of Path Integrals, Trieste-ICTP preprint (IC/80/129) (with E.Keyman)

7) Decay Rate for Supercurrent in Thin Wire, Jour.of Low Temperature Phys. 42, 137- 150 (1981) (with H.Kleinert and N.Ünal).

8) Quantum Mechanics of H-Atom via Path Integrals, Fortschritte der Physik, 30, 401- 435 (1982) (with H.Kleinert).

9) An Upper Limit on the Magnetic Moment of Neutrino, Phys.Rev. D 26, 1794- 1797 (1982) (with Z.Z.Aydìn and A.O.Barut).

10) Lifetime of Superflow in Wide-Angle Helical Texture of He-A; Jour.of Low Temperature Phys. 49, 559-572 (1982) (with N.Ünal).

11) Morse Potential Green's Function with Path Integrals. Phys.Rev. D 28, 2689-2692 (1983).

12) Neutrino and Antineutrino Elastic Scattering and Photoneutrino Reactions, Phys.Rev. D 28, 2872-2874 (1983) (with Z.Z.Aydìn and A.O.Barut).

13) Path Integral Representation of the Symmetric Rosen-Morse Potential, Trieste-ICTP preprint (IC/83/178)

14) Feynman's Formula for a Harmonic Oscillator; Int.Journ. of Theor. Phys., 23, 567- 568 (1984).

15) Path Integrals over the SU(2) Manifold and Related Potentials, Phys.Rev. D 30, 2121-2127 (1984).

16) Path Integral Derivation of the Dirac Propagator, Phys.Rev.Lett. 53, 2355-2357 (1984) (with A.O.Barut).

17) Photoproduction of a Neutrino Pair from an Electron and Astrophysical Implications of Neutrino Emission Processes, Phys.Rev. D 32, 3051-3054 (1985) (with Z.Z.Aydìn and A.O.Barut).

18) On the Path Integral for the Potential V=ar-2 + br2 , Phys.Lett. 112 A, 421-423 (1985).

19) Particle Production in Expanding Universes with Path Integrals, Phys.Rev. D 34, 959- 968 (1986) (with N.Ünal).

20) On the Path Integrations for the Wood-Saxon and Related Potentials,Phys.Lett.119A, 163-167 (1986).

21) Exact Solutions of the Dirac Equation in Spatially Flat Robertson-Walker Space- Times, Phys.Rev. D36, 3705-3711 (1987) (with A.O.Barut).

22) On Path Integrals in Spherical Coordinates, J.Phys.A:Math.Gen. 21, 3389-3392 (1988) (with N.Ünal).

23) Path Integration via Hamilton-Jacobi Coordinates and Applications to Tunneling, Phys.Rev. A 38, 5906-5909 (1988) (with A.O.Barut).

24) Path Integral Formulation of Quantumelectrodynamics from Classical Particle Trajectories, Phys.Reports 172C, 1-32 (1989) (with A.O.Barut).

25) Quantum Treatment of a Class of Time-Dependent Potentials, J.Phys.A:Math.Gen. 22, 4827-4833 (1989).

26) Pair Production in an Electric Field in a Time-Dependent Gauge, Phys.Rev. D41, 1312-1317 (1990) (with A.O.Barut).

27) Path Integral Quantization of the Magnetic Top, Phys.Lett. A 158, 441-444 (1991) (with A.O.Barut).

28) Pair Production in the Time-Dependent Electric Fields, J.of Sov.Laser Research, 13, 241-250(1992) (with S.A.Baran).

29) Path Integrals over the Group Manifolds, J.of Sov. Laser Research, 13, 304-311 (1992).

30) Casimir Force between two Aharonov-Bohm Solenoids, Foundations of Physics, 23, 809-818 (1993) (Special issue devoted to the 65th birthday of BARUT)

31) Casimir Energies of Localized Light and Electrons in Disordered Materials, Phys.Lett., A176, 265-266 (1993) (with M. Tomak).

32) Path-Integral Quantization of the Confined Solution of a Relativistic Two Body Problem, Physica A209, 249-256 (1994) (with A. O. Barut).

33) Particle Production in a Class of Anisotropic Cosmologies, Gen. Relativ. Gravit. 26 (1994) 969-978.

34) slq(2) Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations, J.Phys.A:Math.Gen.28 2395-2402 (1995) (with Ö.F. Dayì)

35) Spontaneous Pair Production in a Magnetic Monopole Field, J.Phys.A:Math.Gen. 28, 5883-5888 (1995).

36) Green Functions for the Potential Barrier V=ch-2? from the Path Integration over SO(1,2) J.Phys.A:Math.Gen., 30, 173-184 (1997) (with H. Ahmedov).

37) q-Schrödinger Equations for V=u2+1/u2 and Morse Potentials in terms of the q- canonical Transformations, Int.J.Mod.Phys.A, 12, 2373-2384 (1997) (with Ö.F. Dayì).

38) A q-oscillator Green Function, J.Math.Phys. 38, 3889-3894 (1997) (with H. Ahmedov).

39) Green Function on the q-symmetric Space Uq(2)/U(1), J.Phys.A:Math.Gen. 31, 5741- 5754 (1998) (with H. Ahmedov)

40) Green Function on the Quantum Plane, J.Phys.A:Math.Gen. 32, 6255-6260 (1999) (with H. Ahmedov)

41) Unitary Representations of the 2-Dimensional Euclidian Groups in the Heisenberg Algebra, J. Phys.A:Math.Gen. 33, 4277-4281 (2000), (with H. Ahmedov).

42) Representations of SU(1,1) in Non-Commutative Space Generated by the Heisenber Algebra, J.Phys.A: Math.Gen. 34, 227-234 (2001), (with H. Ahmedov).

43) Summation Formulae for the Product of the q-Kummer Functions from Eq(2), J.Phys.A:Math.Gen. 34, 1333-1340 (2001) (with H. Ahmedov).

44) Casimir Force between Surfaces Close to each Other, J. Math.Phys., 44, 5487-5503, (2003) (with H. Ahmedov).

45) Casimir Energy Inside a Cavity with Triangular Crossection, J. Math.Phys., 45, 965-977, (2004), (with H. Ahmedov).

46) Casimir Energy for a Wedge with Three Surfaces and for a Pyramidal Cavity, J. Math.Phys., 46, 022303, (2005), (with H. Ahmedov)

47) Casimir Energy in a Conical Wedge and a Conical Cavity, J. Math.Phys., 46, 022304, (2005), (with H. Ahmedov)

48) Regularized Green's Function and Group of Reflection in a Cavity with Triangular Cross Section, Phys.Atom.Nucl., 68, 1621, (2005), (with H. Ahmedov)

1) "Particle Production in the Inflationary Universe with Path Integrals", in "Path Integrals from meV to MeV". pp.414-422, M.C.Gutzwiller et al., eds., World Scientific, Singapore (1986). (with N. Ünal)2) "Aharonov-Bohm Effect and Casimir Interactions, in "New Frontiers in QED and Quantum Optics", pp.451-458, A.O.Barut ed., NATO ASI Series B 232, Plenum, New York (1990).

3) "Vacuum Structures in the Spaces with non Trivial Topologies", in "Proceedings of Regional Conference on Mathematical Physics", pp.246-263, F. Ardalan, H. Arfaei, S. Rouhani eds., Sharif Univ.Tech.Press (1990).

4) "Pair Production in an Electric Field in a Time-Dependent Gauge: A Treatment Parallel to the Cosmological Particle Production", in "Vacuum Structure in Intense Fields" pp.402-406, H.M.Fried and B.Müller eds., NATO ASI series B 255, Plenum, New York (1991).

5) "Methods for Solving Path Integrals and QED from Classical Particle Trajectories ", in "Nonlinear Fields: Classical, Random, Semiclassical" pp. 529-543, P.Garbaczewski and Z.Popowicz eds, World Scientific, Singapore (1991).

6) "Quantum Mechanical Effects of Topological Origin" in "Second International Workshop on Squezzed States and Uncertainity Relations", pp.273-275, Man'ko, D. Han, Y.S. Kim, V.I. Man'ko eds., NASA Conference Publication Series 3219 (1993).

7) "On the Massless Field Production in Anisotropic Spacetimes", (Special issue devoted to the Trakya University International Meeting on Theoretical Physics, 1991), Turkish J. of Physics 17, 1-10 (1993).

8) "Vacuum Decays in External Electromagnetic Fields and in Cosmological Backgrounds", (Special issue devoted to the Trakya University, International Meeting on the Recent Developments on Theoretical Physics, 1993) Turkish J.of Physics, 19, 274-280 (1995).

9) "Quantum Mechanical Motions over the Group Manifolds and Related Potentials", in "Symmetries in Science VII" (Bregenz, 1994) pp. 91-100, B. Gruber ed., Plenum, New York (1995).

10) "Vacuum Structure for Charged Fields in Presence of E-M Potentials and Boundaries" in "Electron Theory and QED, 100 years laters", pp.77-82,, J. Dowling ed., NATO ASI series, Plenum, New York (1997)

11) "q-deformed Kepler and Morse Potentials from q-oscillators", pp.137-144, in "VII. International Conference on Symmetry Methods in Physics," A.N. Sissakian and G.S. Pogosyan eds., JINR, Dubna (1996) (with Ö.F. Dayì).

12) "Quantum Mechanical Problems with q-deformations and over the p-adic Number Fields", pp. 93-97, in "Symmetries in Science IX", B. Gruber and M. Ramek eds., Plenum, New York (1997)

13) "Green Function on the q-Symmetric Space SUq(2)/U(1)", in "New Symmetries in the Fundamental Interactions Theories; IX Max Born Symposium", J. Lukierski ed., PWN Polish Scientific Publication, Warsaw, (with H. Ahmedov) (in press).

14) "q-Schrödinger equations for Kepler and Morse Potentials Consistent with q- harmonic oscillators", pp. 348-360 in "Proceedings of the Barut Memorial Conference" T. Dereli and I. H. Duru eds., Special issue of Tr.J.of Phys., 21, (1997) (with Ö. F. Dayì)

15) "On the Invariant Distance and Green Function for SUq(2), pp.1069- in "Proceeding of 6th International Colloquium on Quantum Groups and Integrable Systems" Prague; Special issue of Czech-J.Phys. 47, pp.1069-1074 (1997) (with H. Ahmedov).

16) "Interference on Charged Particles in a Vector Potential with Vanishing Magnetic Field" pp. 825-830 (Special issue devoted to the IInd Workshop on Macroscopic Electrodynamics, held in Cracow, Poland, 1997); Tr.J.Phys. 23 (1999).

17) "Greens Functions on the Quantum Plane and some q-Special Functions" pp. 432-436 in "Quantum Theory and Symmetries", H.-D. Doebner et al eds. World Scientific, Singapore (2000).

18) "THe Use of Non-Relativistic Path Integrals in Field Theories", in "Fluctuating Paths and Fields", dedicated to Prof. Dr. Hagen Kleinert, W. Janke et. al. eds, World Scientific, Singapore (2001).