Over 100 papers are published in (i) General Relativity and Gravitation, (ii) Quantum Field Theory, and (iii) Applied Mathematics, by myself and co-workers. I shall mention in the following a few of the relatively significant ones, with appropriate comments.

1. A. Das, The Artificial Satellite and the Relativistic Red Shift. Progress of Theoretical Physics (Japan), 18, 554– (1957).

   (Remarks: This letter to the editor was published before the first satellite, Sputnik, was launched. Relevant equations were derived from perturbative solutions of Einstein’s equations in presence of the rotating Earth. Similar equations are utilized today for guidance of GPS (Global Positioning System).)

2. A. Das, Cellular Space-Time and Quantum Field Theory. Nuovo Cimento, 18, 482– (1960).

   (Remarks: Quantum Field Theories were formulated with partial difference equations in the cellular space-time (equivalently, in the lattice space-time with a non-negotiable fundamental length). Divergence problems of the S-matrix elements (except for infrared difficulties) were completely eliminated. Although, mathematically, there exists a discrete subgroup, the relativistic covariance could not be claimed for this formulation.)

3. A. Das, P.S. Florides, and J.L. Synge, F.R.S. Stationary weak gravitational fields to any order of approximation. Proceedings of the Royal Society (London), 263, 451– (1961).

   (Remarks: A mathematically rigorous, thorough, perturbative scheme was developed to tackle Einstein’s interior field equations. (Late Professor J.L. Synge, F.R.S. thought highly of this paper.))

4. A. Das, A class of exact solutions of certain classical field equations in general relativity. Proceedings of the Royal Society (London), 267, 1– (1962).

   (Remarks: Long time ago, Weyl in his study of axially symmetric, static, Maxwell-Einstein equations, showed that a quadratic relationship between the electrostatic potential and gravostatic potential reduces coupled field equations drastically. Majumdar and Papapetrou investigated general static, Maxwell-Einstein equations with whole – squared relationship between two potentials. Equations reduced remarkably to yield exact multi-charged particle solutions. In the present paper, I showed that in presence of a charged, incoherent dust, the equality of charged density with mass density leads to equilibrium among various electric and gravitational forces automatically. Moreover, the mysterious whole-square relationship emerges mathematically.)

5. A. Das, Complex Scalar Field in General Relativity. Journal of Mathematics and Physics (USA), 4, 45– (1963)

   (Remarks: As far as we know, this was the first paper to deal with the coupled Einstein-Maxwell-Klein-Gordon field equations involving three interacting fields. A class of spherically symmetric exact solutions was obtained.)

6. A. Das, Complex Space-Time and Classical Field Theory. Journal of Mathematics and Physics (USA), 7, 45– (1966)
   

   (Remarks: This is the first of three inter-connected papers involving a four-dimensional complex space-time. The metric tensor is taken to be the Hermitian generalization of the Lorentz metric. Classical field equations were developed in the arena of the complex space-time.)

7. A. Das, The Quantized Complex Space-Time and Quantum Theory of Free Fields. Journal of Mathematics and Physics (USA), 7, 61– (1966)
   

   (Remarks: Each of the four complex planes was quantized independently. The expectation of operator-valued wave function yielded Laguerre polynomials. Green’s functions associated with the expectation value of the operator Klein-Gordon equation, were all non-singular. Since divergence difficulties of usual quantum fields theories originate from singular Green’s functions, the quantized space-time yielded a hopeful sign.)

8. A. Das, Complex Space-Time and Geometrization of Electromagnetism. Journal of Mathematics and Physics, 7, 61– (1966)

   (Remarks: Curved complex space-time was formulated. Einstein’s equations extended to the complex space-time are equivalent to field equations in a real eight-dimensional “space-time.” Such an extended space- time, with existence of suitable number of Killing vectors, easily unified electromagnetism and gravitation.)

9. A. Das and C.V. Coffman, A Class of Eigenvalues of the Fine Structure Constant and Internal Energy Obtained from a Class of Exact Solutions of the Combined Klein-Gordon-Maxwell-Einstein Equations. Journal of Mathematics and Physics (USA), 8, 1720– (1967)

   (Remarks: In the spherically symmetric case, the coupled Klein-Gordon-Maxwell-Einstein Equations were reduced to one, second order, semi-linear ordinary differential equation. The differential equation involved one undetermined parameter, namely, the fine structure constant. After imposing initial-boundary values, the mathematical problem became a non-linear eigenvalue problem for the fine structure constant. Denumerably infinite number of eigenvalues were admitted. However, none of these values agreed with the experimentally known value. (The reason for this discrepancy was due to the neglect of the electro-weak gauge field.))

10. A. Das, “Short-Ranged” Scalar Gravity in Einstein’s Theory. Journal of Mathematics and Physics (USA), 12, 232– (1971)

    (Remarks: Einstein’s interior field equations were studied with the restriction of conformal flatness of the metric. Outside the material sources, the field equations could only yield flatness (or no gravitation). However, inside the material sources, the equations yielded a real, massive scalar field equation resembling a non-linear meson field. This field physically represented for a short-ranged gravitational force resembling the so-called fifth force.)

11. A. Das and P. Agrawal, Friedman Universes Containing Wave Fields. General Relativity and Gravitation, 5, 359– (1974)

    (Remarks: In this paper, Friedmann-Robertson-Walker metric containing a massless scalar field was studied. All analytical, exact solutions were derived.
    The paper investigated also the F-R-W metric containing a massive scalar field. In this case, field equations were reduced to a single, non-linear ordinary differential equation. Numerical solutions were presented.)

12. S. Kloster, M.M Som, and A. Das, On the Stationary Gravitational Fields. Journal of Mathematics and Physics (USA), 15, 1096– (1974).

    (Remarks: General stationary, vacuum equations of Einstein were investigated thoroughly. Moreover, studying the +4 (signature) version of the differential equations, gravitational instanton solutions were discovered for the first time.)

13. M. J. Hamilton and A. Das, On the combined Dirac-Einstein-Maxwell field equations. Journal of Mathematics and Physics (U.S.A.), 15, 2026– (1977)

    (Remarks: Field equations involving Einstein-Maxwell equations coupled to a Dirac spinor field was studied for the first time (to our knowledge). A class of exact solutions was discovered.)

14. J. D. Gegenberg and A. Das, Five-Dimensional Cosmological Models With Massless Scalar Fields. Physics Letters, 112A, 427– (1985)

    (Remarks: Cosmological models were constructed from solutions of five-dimensional Einstein equations with a real, massless, non-self-interacting scalar field. For the case of the flat three-space, two classes of exact solutions emerged. One of the solutions imply a power-law type of expansion of the three-space and a contraction of the internal space. The other class produces exponential expansion of the three-space together with an exponential contraction of the internal space.)

15. A. Das, A New Improper Riemann Integral and the Dirac Delta-Function. Indian Journal of Pure and Applied Mathematics, 18, 997– (1987)

    (Remarks: Use of the Dirac delta-function can be mathematically justified by the distribution theory. However, in some papers on theoretical physics, I have used Dirac delta-functions in simplistic manners as physicists do. My colleagues in the Mathematics department did not like such usages. So I tried to find a rigorous definition of the Dirac delta-function within the frame work of Improper Riemann integrals. I found the answer involving the integration by parts. The definition is after all so simple that in can be taught to the second-year undergraduate students!)

16. A. Das, General Solutions of Maxwell-Dirac Equations in 1+ 1-Dimensional “Space-Time” and a Spatially Confined Solutions. Journal of Mathematics and Physics (U.S.A.), 34, 3986– (1993).

    (Remarks: Coupled (classical) Maxwell-Dirac equations were studied in 1+ 1-dimensional “space-time.” (Dirac field was assumed to be massless.) The alternate nomenclature of this model is the classical Schwinger theory. The most general solutions of this coupled system of partial differential equations were discovered. The general solutions comprised of one arbitrary constant and four arbitrary functions. As an example of a particular solution, one involving an exactly confined Dirac field (analogous to a quark) was furnished.))

17. A. Das and P. Smoczynski, Discrete Phase Space I: Finite Difference Operators and Lattice SchrÖdinger Equation. Foundations of Physics Letters, 7, 21-, (1994)

    (Remarks: A new representation of quantum mechanics involving finite difference operators was presented. The time-dependent Schrödinger wave equation was furnished as a partial difference-differential equations. I emphasize that this representation is exact and not a numerical approximation.)

18. A. Das and P. Smoczynski, Discrete Phase Space II: Relativistic Lattice Wave Equations and Divergence-free Green’s Functions. Foundations of Physics Letters, 7, 127– (1994)

    (Remarks: Following the preceding paper (no. 17), the relativistic lattice Klein-Gordon equations, Dirac equations, electromagnetic equations were presented as partial difference equations. (The equations were covariant under the continuous Poincaré transformations.) It was proved that important Green’s functions associated with these fields equations were non-singular. In future papers, I intend to use these equations to eliminate divergence problems of quantum field theories. (See the reprints.)

19. A. Das, N. Tariq, and D. Aruliah, and T. Biech, Spherically symmetric collapse of an anisotropic fluid body into an exotic black hole. Journal of Mathematics and Physics (USA), 38, 4202– (1997)

    (Remarks: Einstein’s spherically symmetric field equations were investigated. The energy-momentum-stress tensor matrix had the Segre characteristic [1, (1, 1), 1]. Usual junctions conditions were satisfied on the boundary of the collapsing material body. Weak energy conditions were satisfied prior to the collapse of the boundary inside the event horizon. However, inside, the event horizon, energy conditions were violated and drastic transitions into four exotic phases occurred. (These exotic states are not encountered in the exterior universe.))

20. A. Das and S. Kloster, Analytical solutions of a spherically symmetric collapse of anisotropic fluid body into a regular black hole. Physical Review D, 62, 104002– (2000)

    (Remarks: Einstein’s spherically symmetric field equations were investigated with a Tolman-Bondi coordinate system. The energy-momentum-stress matrix had the Segre characteristic [1, (1,1), 1]. On the boundary of the collapsing body, Synge’s and Israel’s junction conditions were satisfied. Inside the material, all the energy conditions were satisfied. The interior metric were joined very smoothly to the Kruskal metric of domains I and II.)

21. A. Das, Discrete Phase Space - I, Canadian Journal of Physica, 88: 73-91 (2010)

22. A. Das, Discrete Phase Space - II, Canadian Journal of Physica, 88: 93-109 (2010)

23. A. Das, Discrete Phase Space - III, Canadian Journal of Physica, 88: 111-130 (2010)