(Updated December 2009)
Books:
A. Mostafazadeh, “Dynamical Invariants, Adiabatic Approximation and the Geometric Phase,” Nova Science Publications, New York, 2001.
A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, and J. Zwanziger, “The Geometric Phase in Quantum Systems,” Springer-Verlag, New York, 2003.
Journal Publications (Covered by Science Citation Index):
During Undergraduate Studies (1985-89)
1. M. Arýk, E. Hizel, and A. Mostafazadeh, "The Schwarzschild Solution in Non-Abelian Kaluza-Klein Theories," Class. Quantum Grav. 7, 1425-32 (1990).
During Graduate Studies (1989-94)
2. A. Bohm, L. J. Boya, A. Mostafazadeh, and G. Rudolph, “Classification Theorem for Principal Fibre Bundles, Berry's Phase, and Exact Cyclic Evolution,” J. Geom. Phys. 12, 13-28 (1993.
3. A. Mostafazadeh and A. Bohm, “Topological Aspects of the Non-Adiabatic Berry Phase,” J. Phys. A: Math. Gen. 26, 5473-5479 (1993); hep-th/9309060.
4. A. Mostafazadeh, “Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions and a Proof of the Index Theorem via Gaussian Superdeterminants,” J. Math. Phys. 35, 1095-1124 (1994); hep-th/9309059.
5. A. Mostafazadeh, “Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schrödinger Equation, J. Math. Phys. 35, 1125-1138 (1994); hep-th/9309061.
6. A. Bohm and A. Mostafazadeh, “The Relation between the Berry and the Anandan-Aharonov Connections for U(N) bundles,” J. Math. Phys. 35, 1463-1470 (1994).
Since Receiving Ph.D. (1994 - present)
7. A. Mostafazadeh, “Spectrum Degeneracy of General (p=2)--Parasupersymmetric Quantum Mechanics and Parasupersymmetric Topological Invariants,” Int. J. Mod. Phys. A 11, 1057-1076 (1996); hep-th/9410180.
8. A. Mostafazadeh, “Geometric Phase, Bundle Classification, and Group Representation,” J. Math. Phys. 37, 1218-1233 (1996); Erratum J. Math. Phys. 40, 3697 (1999); hep-th/9312173.
9. A. Mostafazadeh, “Para-Generalization of Peierls Bracket Quantization,” Int. J. Mod. Phys. A 11, 2941-2955 (1996); hep-th/9508061.
10. A. Mostafazadeh, “Parabose-Parafermi Supersymmetry,” Int. J. Mod. Phys. A 11, 2957-2975 (1996); hep-th/9508106.
11. A. Mostafazadeh, “Scalar Curvature Factor in the Schrödinger Equation and Scattering on a Curved Surface,” Phys. Rev. A 54, 1165-1170 (1996); hep-th/9602095.
12. V. Karimipour and A. Mostafazadeh, “Lattice Topological Field Theory on Non-Orientable Surfaces,” J. Math. Phys. 38 , 49-66 (1997); hep-th/9508041.
13. A. Mostafazadeh, “Quantum Adiabatic Approximation and the Geometric Phase,” Phys. Rev. A 55, 1653-1664 (1997); hep-th/9606053.
14. A. Mostafazadeh, “Adiabatic Product Expansion,” Phys. Lett. A 228, 7-12 (1997); quant-ph/9606032.
15. A. Mostafazadeh, “Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators,” Int. J. Mod. Phys. A 12, 2725-39 (1997); hep-th/9603163.
16. A. Mostafazadeh, “Comment on: Cyclic Quantum Evolution Dependence on the Hamiltonian and Geometric Phase,” Phys. Rev. A 55, 4640 (1997); quant-ph/9606022.
17. A. Mostafazadeh, “Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators,” Phys. Rev. A 55, 4084-89 (1997); quant-ph/9611053.
18. A. Mostafazadeh, “Quantum Canonical Transformations and Exact Solution of the Schrödinger Equation,” J. Math. Phys. 38, 3489-96 (1997); quant-ph/9611052.
19. A. Mostafazadeh, “Quantum Adiabatic Approximation, Quantum Action, and Berry's Phase,” Phys. Lett. A 232, 395-98 (1997); quant-ph/9606021.
20. A. Mostafazadeh, “Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems,” J. Phys. A: Math. Gen. 30, 7525-35 (1997); quant-ph/9608031.
21. A. Mostafazadeh, “Exact Semiclassical Evolutions in Relativistic and Nonrelativistic Scalar Quantum Mechanics and Quantum Cosmology,” Nucl. Phys. B 509, 529-555 (1998); gr-qc/9701061.
22. A. Mostafazadeh, “Time-Dependent Diffeomorphisms as Quantum Canonical Transformations and the Time-Dependent Oscillator,” J. Phys. A: Math. Gen. 31, 6495-6503 (1998); quant-ph/9807002.
23. A. Mostafazadeh, “Two-Component Formulation of the Wheeler-DeWitt Equation,” J. Math. Phys. 39, 4499-4512 (1998); gr-qc/9610012.
24. A. Mostafazadeh, “Relativistic Adiabatic Approximation and Geometric Phase,” J. Phys. A: Math. Gen. 31, 7829-45 (1998); quant-ph/9807003.
25. A. Mostafazadeh, “Non-Abelian Geometric Phase, Floquet Theory, and Dynamical Invariants,” J. Phys. A: Math. Gen. 31, 9975-82 (1998); quant-ph/9810064.
26. A. Mostafazadeh, “Generalized Adiabatic Product Expansion: A nonperturbative method of solving time-dependent Schrödinger equation,” J. Math. Phys., 40, 3311-26 (1999); quant-ph/9904026.
27. A. Mostafazadeh, “Noncyclic Geometrical Phase and Its Non-Abelian Generalization,” J. Phys. A: Math. Gen. 32, 8157-8171 (1999); quant-ph/9909093.
28. A. Mostafazadeh, “Comment on Identical Motion in Classical and Quantum Mechanics,” Phys. Rev. A 60, 5144-5145 (1999); quant-ph/9909092.
29. A. Mostafazadeh, “Perturbative Calculation of the Adiabatic Geometric Phase and a Particle in a Well with Moving Walls,” J. Phys. A: Math. Gen. 32, 8325-8340 (1999); quant-ph/9910104.
30. A. Mostafazadeh, “A new class of adiabatic cyclic states and geometric phases for Non-Hermitian Hamiltonians,” Phys. Lett. A 264, 11-17 (1999); quant-ph/9911003.
31. A. Mostafazadeh and K. Aghababei Samani, “Topological Symmetries,” Mod. Phys. Lett. A 15, 175-184 (2000); hep-th/0003108.
32. A. Mostafazadeh, “Comment on the Possibility of a Geometric Constraint in the Schrödinger quantum mechanics,” Mod. Phys. Lett. A 15, 2129-2130 (2000); quant-ph/0012027.
33. K. Aghababei Samani and A. Mostafazadeh, “Quantum Mechanical Symmetries and Topological Invariants,” Nucl. Phys. B 595, 467-492 (2001); hep-th/0007008.
34. A. Mostafazadeh, “Supersymmetric Dynamical Invariants,” J. Phys. A: Math. Gen. 34, 4493-4506 (2001); quant-ph/0104071.
35. A. Mostafazadeh, “Variational Sturmian Approximations: A nonperturbative method of solving time-independent Schrödinger equation,” J. Math. Phys. 42, 3372-3389 (2001); quant-ph/0105047.
36. A. Mostafazadeh, “Geometric Phases, Symmetries of Dynamical Invariants, and Exact Solution of the Schrödinger equation,” J. Phys. A: Math. Gen. 34, 6325-6338 (2001); quant-ph/0101010.
37. A. Mostafazadeh, “On the Dynamical Invariants and the Geometric Phase for a General Spin System in a Changing Magnetic Field,” Phys. Lett. A 287, 187-189 (2001); quant-ph/0107063.
38. A. Mostafazadeh, “On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry,” J. Phys. A: Math. Gen. 34, 8601-8609 (2001); math-ph/0110013.
39. A. Mostafazadeh, “Pseudo-Hermiticity versus PT-Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian,” J. Math. Phys. 43, 205-214 (2002); math-ph/0107001.
40. A. Mostafazadeh, “On a Z_3-Graded Generalization of the Witten Index,” Nucl. Phys. B 624, 500-508 (2002); hep-th/0112069.
41. K. Aghababei Samani and A. Mostafazadeh, “On the Statistical Origin of Topological Symmetries,” Mod. Phys. Lett. A 17, 131-140 (2002); hep-th/0105013.
42. A. Mostafazadeh, “Pseudo-Hermiticity versus PT-Symmetry II: A complete characterization of non-Hermitian Hamiltonians with a real spectrum,” J. Math. Phys. 43, 2814-2816 (2002); math-ph/0110016.
43. A. Mostafazadeh, “Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries,” J. Math. Phys. 43, 3944-3951 (2002); math-ph/0203005.
44. A. Mostafazadeh, “Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermitian Hamiltonians,” Nucl. Phys. B 640, 419-434 (2002); math-ph/0203041.
45. A. Mostafazadeh, “On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension,” Mod. Phys. Lett. A 17, 1973-1977 (2002); math-ph/0204013.
46. A. Mostafazadeh, “Pseudo-Hermiticity for a Class of Nondiagonalizable Hamiltonians,” J. Math. Phys. 43, 6343-6352 (2002); math-ph/0207009; Erratum: ibid, 44, 943 (2003); math-ph/0301030.
47. A. Mostafazadeh, “Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations,” Class. Quantum Grav. 20, 155-171 (2003); math-ph/0209014.
48. A. Mostafazadeh, “Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries,” J. Math. Phys. 44, 974-989 (2003); math-ph/0209018.
49. A. Mostafazadeh, “Exact PT-Symmetry Is Equivalent to Hermiticity,” J. Phys. A: Math. Gen. 36, 7081-7091 (2003); quant-ph/0304080.
50. A. Mostafazadeh, “Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology,” Ann. Phys. (New York) 309, 1-48 (2004); gr-qc/0306003.
51. A. Mostafazadeh, “Time-Dependent Hilbert Spaces, Geometric Phases, and Generalized Covariance in Quantum Mechanics,” Phys. Lett. A 320, 375-382 (2004); quant-ph/0306200.
52. A. Mostafazadeh, “Pseudo-Unitary Operators and Pseudo-Unitary Quantum Qynamics,” J. Math. Phys. 45, 932-946 (2004); math-ph/0302050.
53. A. Mostafazadeh, “Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions,” J. Phys. A: Math. Gen. 37, 10193-10207 (2004); quant-ph/0404025.
54. A. Mostafazadeh and A. Batal, “Physical Aspects of Pseudo-Hermitian and PT-Symmetric Quantum Mechanics,” J. Phys. A: Math. Gen. 37, 11645-11679 (2004); quant-ph/0408132.
55. A. Mostafazadeh, “Pseudo-Hermitian Description of PT-Symmetric Systems Defined on a Complex Contour,” J. Phys. A: Math. Gen. 38, 3213-3234 (2005); quant-ph/0410012.
56. A. Mostafazadeh, “Comment on Quartic Anharmonic Oscillator and Non-Hermiticity,” Phys. Rev. A 71, 046101 (2005).
57. A. Mostafazadeh, “PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model,” J. Phys. A: Math. Gen. 38, 6557-6569 (2005); quant-ph/0411137.
58. A. Mostafazadeh, “Classical and Quantum Fermions Linked by an Algebraic Deformtion,” Int. J. Geom. Meth. Mod. Phys. 2, 777-782 (2005); math-ph/0312065.
59. A. Mostafazadeh, “Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States,” J. Math. Phys. 46, 102108 (2005), 16 pages; quant-ph/0506094.
60. A. Mostafazadeh, “A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields,” Int. J. Mod. Phys. A 21, 2553-2572 (2006); quant-ph/0307059.
61. A. Mostafazadeh, “Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential,” J. Phys. A: Math. Gen. 39, 10171-10188 (2006); quant-ph/0508195.
62. A. Mostafazadeh, “Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein’s field equation,” J. Math. Phys. 47, 072103 (2006), 11 pages; quant-ph/0603023.
63. A. Mostafazadeh, “Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential,” Phys. Lett. A 357, 177-180 (2006); quant-ph/0603091.
64. A. Mostafazadeh and F. Zamani, “Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry,” Ann. Phys. (N.Y.) 321, 2183-2209 (2006); quant-ph/0602151.
65. A. Mostafazadeh and F. Zamani, “Quantum Mechanics of Klein-Gordon Fields II: Relativistic Coherent States,” Ann. Phys. (N.Y.), 321, 2210-2241 (2006); quant-ph/0602161.
66. A. Mostafazadeh, “Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?”, J. Math. Phys. 47, 092101 (2006), 7 pages; quant-ph/0605110.
67. A. Mostafazadeh, “Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity,” Czech J. Phys. 56, 919-933 (2006); quant-ph/0606173.
68. A. Mostafazadeh, “Delta-Function Potential with a Complex Coupling,” J. Phys. A: Math. Gen. 39, 13495-13506 (2006); quant-ph/0606198.
69. A. Mostafazadeh, “Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator,'' Phys. Lett. B 650, 208-212 (2007); arXiv:0706.1872.
70. A. Mostafazadeh, “Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics,” Phys. Rev. Lett. 99, 130502 (2007), 4 pages; arXiv:0706.3844.
71. A. Mostafazadeh, “Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator,” Phys. Rev. D 76, 067701 (2007), 4 pages; arXiv:0708.3978.
72. A. Mostafazadeh and F. Loran, “Propagation of Electromagnetic Waves in Linear Media and Pseudo-Hermiticity,” Europhys. Lett. 81, 10007 (2008), 6 pages; arXiv:physics/0703080.
73. A. Mostafazadeh, “QT-Symmetry and Weak Pseudo-Hermiticity,” J. Phys. A: Math. Theo., 41, 055304 (2008), 8 pages; arXiv:0710.4879.
74. A. Mostafazadeh, “Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians,” J. Phys. A: Math. Theo., 41, 244017 (2008), 5 pages; arXiv:0707.3075.
75. H. Mehri-Dehnavi and A. Mostafazadeh, “Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation,” J. Math. Phys. 49, 082105 (2008), 17 pages; arXiv:0807.3405.
76. A. Mostafazadeh, “On Hamiltonians Generating Optimal-Speed Evolutions,” Phys. Rev. A 79, 014101 (2009), 4 pages; arXiv:0804.4755.
77. A. Mostafazadeh and H. Mehri-Dehnavi, “Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions,” J. Phys. A 42, 125303 (2009), 27 pages; arXiv:0901.3563.
78. F. Zamani and A. Mostafazadeh, “Quantum Mechanics of Proca Fields,” J. Math. Phys. 50, 052302 (2009), 35 pages; arXiv:0805.1651.
79. A. Mostafazadeh, “Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies,” Phys. Rev. Lett., 102, 220402 (2009), 4 pages; arXiv:0901.4472.
80. A. Mostafazadeh, “Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides,” Phys. Rev. A 80, 032711 (2009); arXiv:0908.1713.
81. A. Mostafazadeh, “Pseudo-Hermiticity and Electromagnetic Wave Propagation in Dispersive Media,” Phys. Lett. A 374, 1307-1310 (2010); arXiv:1001.2675.
82. H. Mehri-Dehnavi, A. Mostafazadeh, and A. Batal, “Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions,” J. Phys. A, to appear; arXiv:1002.1221.
Articles Published in Conference Proceedings Covered by Science Citation Index
83. A. Mostafazadeh, “Two-Component Formulation of the Wheeler-DeWitt Equation for FRW-Massive Scalar Field Minisuperspace,” Particles and the Universe, Proceedings of the Twelfth Lake Louise Winter Institute, held in Lake Lousie, Canada, Feb. 16-22, 1997, editors: A. Astbury, B. A. Campbell, F. C. Khanna, and J. L. Pinfold, World Scientific, 1998, pp. 545-551.
84. A. Mostafazadeh and K. Aghababaei Samani, “Topological Generalizations of Supersymmetry” Nucl. Phys. B (Proc. Suppl.) 104, 251-251 (2002), contributed to the conference on Quantum Gravity and Spectral Geometry, held in Naples, Italy, July 1-6, 2001.
85. A. Mostafazadeh, “Z_n-Graded Topological Generalizations of Supersymmetry and the Orthofermion Algebra,” Institute of Physics Conference Series 173, 459-462 (2003), Group 24: Physical and Mathematical Aspects of Symmetries, Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, held in Paris, France, 15-20 July 2002, editors: J.-P. Gazeau, R. Kerner, J.-P. Antoine, S. Metens, and J.-Y. Thibon; hep-th/0303094.
86. A. Mostafazadeh, “Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?” Czech J. Phys. 53, 1079-1084 (2003), contributed to 12th International Colloquium on Quantum Groups and Integrable Systems, held in Prague, June 15-17, 2003; quant-ph/0308028.
87. A. Mostafazadeh, “Wave Function of the Universe and Its Meaning,” Czech J. Phys. 54, 93-99 (2004), contributed to the 1st International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, held in Prague, June 19-20, 2003; gr-qc/0308029.
88. A. Mostafazadeh, “PT-Symmetric Quantum Mechanics: A precise and consistent formulation,” Czech J. Phys. 54, 1125-1132 (2004), contributed to the 2nd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, held in Prague, June 15-17, 2004; quant-ph/0407213.
89. A. Mostafazadeh, “Pseudo-Hermitian Supersymmetry: A brief review,” Czech J. Phys. 54, 1371-74 (2004), contributed to 13th International Colloquium on Quantum Groups and Integrable Systems, held in Prague, June 17-19, 2004.
90. A. Mostafazadeh, “Pseudo-Hermiticity, PT-Symmetry, and the Metric Operator,” Czech J. Phys. 55, 1157-1160 (2005), contributed to the 3rd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, held in Istanbul, June 20-22, 2005; quant-ph/0508214.
91. A. Mostafazadeh, “Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications,” Pramana-J. Phys. 73, 269-277 (2009), contributed to Homi Bhabha Centenary Conference on Non-Hermitian Hamiltonians in Quantum Physics (8th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics), held in Mumbai, January 13-16, 2009, pdf.
Articles Published in other Conference Proceedings
92. A. Mostafazadeh, “Topology of Parameter Space Bundle and the Non-Adiabatic Berry Phase”, Group Theoretical Methods in Physics, Proceedings of the XIX International Colloquium, held in Salamanca, Spain, June 1992, editors: M. A. del Olmo, M. Santander, and J. Mateos-Guilarte, vol. II, pp. 471-4.
93. A. Mostafazadeh, “A Brief Review of Fibre Bundles and Their Classification,” Integrable Systems, Quantum Groups, and Quantum Field Theories, NATO ASI Series, editors: L. A. Ibort and M. A. Rodriguez, Kluwer Academic Publishers, 1993, pp. 408-15.
94. A. Mostafazadeh, “Quantization of Paraclassical Systems of order p=2 and Parabose- Parafermi Supersymmetry,” Turkish J. Phys. 21, 478-483 (1997), contributed to the Barut Memorial Conference on Group Theory in Physics, held in Edirne, Turkey, Dec. 22-29, 1995.
95. A. Mostafazadeh, “A New Semiclassical Perturbation Theory,” Proceedings of 7th Canadian Conference on General Relativity and Relativistic Astrophysics, held in Calgary, Canada, June 4-7, 1997, University of Calgary Press, 1998.
96. A. Mostafazadeh, “A Non-Perturbative Solution of Time-Dependent Schrödinger Equation, Generalized Adiabatic Approximation, and the q-Bracket,” contributed to Quantum Groups: Deformations and Contractions, held in Istanbul, Turkey, September 17-24, 1997, appeared in the proceedings of the conference.
97. A. Mostafazadeh, “Cosmological Adiabatic Geometric Phase of a Scalar Field in a Bianchi Spacetime,” Turkish J. Phys. 24, 411-428 (2000), contributed to the IX. Regional Conference on Mathematical Physics, held in Istanbul, Turkey, August 8-14; gr-qc/0101087, pdf.
98. A. Mostafazadeh and K. Aghababaei Samani, “Topological Quantum Symmetries: A brief introduction” Proceedings of the Sixth International Wigner Symposium, Volume 1, 375-379, Boðaziçi University Press 2002.
99. A. Mostafazadeh, “Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology,” Proceedings TH2002 Supplement, Birkhause Verlag, Basel, (2003) 219-228, contributed to the Theoretical Physics 2002 conference held in Paris, France, July 22-27, 2002; gr-cq/0205049.
100. A. Mostafazadeh and S. Özçelik, “Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems,” Turkish J. Phys. 30, 437-443 (2006), contributed to the 5th Worksop on Quantization, Dualities, and Integrable Systems, held in Pamukkale University, Denizle, Turkey, 23-27 January, 2006; quant-ph/0607120 ; pdf.
Other Papers
101. A. Mostafazadeh, “On Quantizing Gravity and Geometrizing Quantum Mechanics,” Iranian J. Phys. Research 5, 53-58 (2005).