A. Shadi Tahvildar-Zadeh
Professor of Mathematics
Rutgers, The State University of New Jersey
Hill Center, Busch Campus
Piscataway NJ 08854
Phone: (848) 445-7955
Fax: (732) 445-5530
Email: shadit@math.rutgers.edu
Office: 436 Hill Center, Busch
Research interests: Mathematical Physics (special and general relativity, quantum mechanics).
Publications:
(with M. Kiessling) ``Noetherian Conservation Laws for Photons,'' (2025) 23 pages. [arXiv:2503.03271]
(with S. Dasgupta & C. Khurana) ``One-dimensional hydrogenic ions with screened nuclear Coulomb field," to appear in Involve. [arXiv:2312.04033]
(with E. Kapengut, M. Kiessling, & E. Ling) ``On the discrete Dirac spectrum of general-relativistic hydrogenic ions with anomalous magnetic moment," Ann. Henri Poincare (2025). [arXiv:2401.15802]
(with L. Frolov & S. E. Leigh) ``On the relativistic quantum mechanics of a photon between two electrons in 1+1 dimensions," Letters in Mathematical Physics 115 (1), 9. [arXiv:2312.06019] (2025)
(with L. Frolov & S. E. Leigh) ``Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension," J. Math. Phys. 65, 062901 (2024) [arXiv:2307.03149]
(with Aditya Agashe & Ethan Lee) On the joint evolution problem for a scalar field and its singularity, Involve 17 (2024), No. 1, 163–182 (2023). [arXiv:2211.00452]
(with M. Kiessling and Maaneli Derakhshani) Covariant guiding laws for fields, Pure and Applied Mathematics Quarterly, 20(4), 1923-1972. [arXiv:2110.09683]
(with M. Kiessling and E. Ling) ``On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetime," J. Math. Phys. 63, 112301 (2022) [arXiv:2112.00073]
(with M. Kiessling and E. Ling) The point spectrum of the Dirac Hamiltonian on the zero-gravity Kerr-Newman spacetime, The Sixteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories: Proceedings of the MG16 Meeting on General Relativity; 5–10 July 2021. (2023) [arXiv:2111.01960]
(with M. Kiessling and E. Toprak) On the Dirac operator for a test electron in a Reissner--Weyl--Nordström black hole spacetime, Gen. Rel. & Grav. 53, (2021), 21 pages. [arXiv:2009.07358]
(with M. Kiessling and E. Toprak) On general-relativistic hydrogen and hydrogenic ions, J. Math. Phys. 61, (2020), 22 pages. [arXiv:2006.08587]
(with M. Kiessling and M. Lienert) A Lorentz-Covariant Interacting Electron-Photon System in One Space Dimension, Lett. Math. Phys. 110, (2020), 36 pages. [arXiv:1906.03632]
(with M. Kiessling) The Einstein-Infeld-Hoffmann legacy in mathematical relativity II. Quantum laws of motion, Int. J. Mod. Phys. 28, (2019), 14 pages. [arXiv:1906.00479]
(with M. Kiessling) The Einstein-Infeld-Hoffmann legacy in mathematical relativity I. The classical motion of charged point particles, Int. J. Mod. Phys. 28, (2019), 16 pages. [arXiv:1906.00308]
(with A. Burtscher and M. Kiessling) Weak Second Bianchi Identity for Spacetimes with Timelike Singularities, Class. Quant. Grav. 38:18, (2021), 31 pages. [arXiv:1901.00813]
(with M. Kiessling) On the Quantum Mechanics of a Single Photon, Jour. Math. Phys. 59, 112302 (2018), 34 pages. [arXiv:1801.00268]
(with S. Beheshti) Integrability and Vesture for Harmonic Maps into Symmetric Spaces, Rev. Math. Phys. 28:03 1650006 (2016), 44 pages. [arXiv: 1209:1383].
(with M. Kiessling) A novel quantum-mechanical interpretation of the Dirac equation, Jour. Phys. A (2016), 54 pages. [arXiv:1411.2296]
(with M. Kiessling) Dirac's point electron in the zero-gravity Kerr--Newman world, in Quantum Mathematical Physics, F. Finster, J. Kleiner, C. Roken, and J. Tolksdorf, eds., Birkhauser Basel, 2016. [arXiv: 1505.05552]
On a zero-gravity limit of the Kerr-Newman spacetimes and their electromagnetic fields, Jour. Math. Phys. 56, 042501 (2015) [arXiv:1410.0416]
(with Michael Kiessling) The Dirac point electron in zero-gravity Kerr--Newman spacetime Jour. Math. Phys. 56, 042303 (2015) [arXiv:1410.0419]
(with S. Beheshti) Dressing with control: Using integrability to generate desired solutions to Einstein's equations. in The sine-Gordon Model and its Applications, Springer International Publishing, 2014. 207-231. [arXiv:1312.5253]
On the static spacetime of a single point charge, Reviews in Mathematical Physics, 23 No. 3 (2011) 1-38. [arXiv:1012.1400]
(with M. Kiessling) On the relativistic Vlasov-Poisson system, Indiana University Math Journal, Vol. 57, No. 7 (2008), 3177—3207 [arXiv:0708.1760v3].
(with N. Burq, F. Planchon & J. Stalker) Strichartz estimates for wave and Schroedinger equations with potentials of critical decay, Indiana University Math Journal, Vol. 53, No. 6 (2004), 1667-1682 [arXiv:math.AP/0401019].
(with J. Stalker) Scalar waves on naked singularity backgrounds, Classical and Quantum Gravity, Vol. 21, 2831--2848 (2004) [arXiv:gr-qc/0401011].
(with N. Burq, F. Planchon & J. Stalker) Strichartz estimates for the wave and Schroedinger equations with the inverse-square potential, Journal of Functional Analysis Vol. 203, 519--549, (2003). [arXiv:math/0207152]
(with J. Stalker & F. Planchon) Dispersive Estimate for the Wave Equation with the Inverse-Square Potential, Discrete and Continuous Dynamical Systems, Vol. 9, No. 6, 1387--1400, (2003).
(with J. Stalker & F. Planchon) L^p Estimates for the Wave Equation with the Inverse-Square Potential, Discrete and Continuous Dynamical Systems, Vol. 9, N0. 2, 427--442, (2003).
(with Yan Guo) Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics, Contemporary Mathematics, Vol. 238, 151--161, (1999). [arXiv:math/9807136]
Relativistic and non-relativistic elastodynamics with small shear strains, Ann. Inst. H.~Poincare Phys. Theor., Vol. 69, No. 3, 275--307, (1998).
(with T. Cazenave & J.~Shatah) Harmonic maps of the hyperbolic space and development of singularities for wave maps and Yang-Mills fields, Ann. Inst. H.~Poincare Phys. Theor. Vol. 68, N0. 3, 315--349, (1998).
(with A. Schlatter & M.~Struwe) Global existence of the equivariant Yang-Mills flow in four dimensions, Amer. J. Math. , Vol. 120, 117--128, (1998).
(with J. Shatah) On the stability of stationary wave maps, Comm. Math. Phys., Vol. 185, 231--256, (1997).
(with J. Shatah) On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math., Vol. XLVII, 719-754, (1994).
(with D. Christodoulou) On the asymptotic behavior of spherically symmetric wave maps, Duke Math. Jour., Vol. 71, No. 1, 31-69, (1993).
(with D. Christodoulou) On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math., Vol. XLVI, 1041-1091, (1993).
(with J. Shatah) Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds, Comm. Pure Appl. Math., Vol. XLV, 947-971, (1992).
Links:
Interacting Electron-Photon System
Last updated: February 2023
