Asenjo, F. A., & Hojman, S. A. (2023). Timedomain supersymmetry for massless scalar and electromagnetic fields in anisotropic cosmologies. Phys. Scr., 98(10), 105302.
Abstract: It is shown that any cosmological anisotropic model produces supersymmetric theories for both massless scalar and electromagnetic (abelian) fields. This supersymmetric theory is the timedomain analogue of a supersymmetric quantum mechanics algebra theory. In this case, the variations of the anisotropic scale factors of the Universe are responsible for triggering the supersymmetry. For scalar fields, the superpartner fields evolve in two different cosmological scenarios (Universes). On the other hand, for propagating electromagnetic fields, supersymmetry is manifested through its polarization degrees of freedom in one Universe. In this case, polarization degrees of freedom of electromagnetic waves, which are orthogonal to its propagation direction, become superpartners from each other. This behavior can be measured, for example, through the rotation of the plane of polarization of cosmological light.

Asenjo, F. A., & Mahajan, S. M. (2015). Relativistic quantum vorticity of the quadratic form of the Dirac equation. Phys. Scr., 90(1), 4 pp.
Abstract: We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the FeynmanGellMann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and nonrelativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system.

Hojman, S. A., & Asenjo, F. A. (2020). Classical and Quantum Dispersion Relations. Phys. Scr., 95(8), 7 pp.
Abstract: It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion relation, but they differ in the general case. The dispersion relations may also coincide when additional assumptions are made, such as WKB or eikonal approximations, for instance. This general result also holds for nonquantum wave equations derived from classical counterparts, such as in ray and wave optics, for instance. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.

Hojman, S. A., & Asenjo, F. A. (2024). Cosmological electromagnetic Hopfions. Phys. Scr., 99(5), 055514.
Abstract: It is shown that any mathematical solution for null electromagnetic field knots in flat spacetime is also a null field knotted solution for cosmological electromagnetic fields. This is obtained by replacing the time t > tau = integral dt/a, where a = a(t) is the scale factor of the Universe described by the FriedmanLemaitreRobertsonWalker (FLRW) cosmology, and by adequately rewriting the (empty flat spacetimes) electromagnetic fields solutions in a medium defined by the FLRW metric. We found that the dispersion (evolution) of electromagnetic Hopfions is faster on cosmological scenarios. We discuss the implications of these results for different cosmological models.

Hojman, S. J., MoyaCessa, H. M., SotoEguibar, F., & Asenjo, F. A. (2021). Timedependent harmonic oscillators and SUSY in time domain. Phys. Scr., 96(12), 125218.
Abstract: We show that the timedependent harmonic oscillator has a repulsive or inverted oscillator as a time domain SUSYlike partner. Examples of several kinds of supersymmetrical time dependent frequency systems are presented.

Qadir, A., Asenjo, F. A., & Mahajan, S. M. (2014). Magnetic field seed generation in plasmas around charged and rotating black holes. Phys. Scr., 89(8), 7 pp.
Abstract: Previous work by the authors introduced the possibility of generating seed magnetic fields by spacetime curvature and applied it in the vicinity of a Schwarzschild black hole. It was pointed out that it would be worthwhile to consider the effect in other background geometries and particularly in the vicinity of a rotating black hole, which is generically to be expected, astrophysically. In this paper that suggestion is followed up and we calculate generated magnetic field seed due to ReissnerNordstrom and Kerr spacetimes. The conditions for the drive for the seed of a magnetic field is obtained for charged black holes, finding that in the horizon the drive vanishes. Also, the psi Nforce produced by the Kerr black hole is obtained and its relation with the magnetic field seed is discussed, producing a more effective drive.
