Space-Time Algebra of Sedeons

This book is a comprehensive guide to the space-time algebra of sixteen-component values "sedeons". This algebra is designed to provide a compact representation of equations that describe various physical systems. The book considers the symmetry of physical quantities concerning the operations of spatial and temporal inversion. This approach allows the formulation of a wide class of mathematical physics equations within a unified framework and enables the generalization of these equations for essential problems in electrodynamics, hydrodynamics, plasma physics, field theory, and quantum mechanics. In particular, it is shown that the broken symmetry between electricity and magnetism in electrodynamics equations is a result of choosing an asymmetric representation of these phenomena. The sedeonic algebra enables the formulation of Maxwell-like equations for the fields with a nonzero mass of quantum, which facilitates the calculation of energy for baryon-baryon interaction and the semi-classical interpretation of this interaction. It also allows one to generalize the hydrodynamics equations for the case of vortex turbulent flows and for a hydrodynamic two-fluid model of electron-ion plasma.

• This book provides original space-time algebra of 16-component sedeons.
• It contains novel results on electrodynamics, hydrodynamics, and plasma physics.
• The topics of field theory and quantum mechanics are also included.

Professor Victor Mironov is the leading researcher at the Institute for Physics of Microstructures of the Russian Academy of Sciences, doctor of sciences. The area of scientific interests is solid state physics and mathematical physics. The textbook V.L. Mironov "Fundamentals of scanning probe microscopy" (Mosсow, Technosphera, 2004) is well known among the specialists in condensed matter physics. Recent publications

1. V.　L. Mironov, S.　V. Mironov – Sedeonic equations in field theory, Advances in Applied Clifford Algebras, 30(3), 44 1-26 (2020).
2. V.　L. Mironov, S.　V. Mironov – Generalized sedeonic equations of hydrodynamics, European Physical Journal Plus, 135(9), 708 1-17 (2020).
3. V.　L. Mironov, O.　L.　Ermolaeva, Pinning of domain wall in composite ferromagnetic nanowire consisting of two layers with distinct magnetic anisotropy, IEEE Transactions on Magnetics, 56(10), 1100106 (2020).
4. E.V.Skorokhodov, M.V.Sapozhnikov, O.L.Ermolaeva, N.S.Gusev, A.A.Fraerman, V.L.Mironov, Magnetic resonance force spectroscopy of multilayer films Co/Pt with perpendicular magnetic anisotropy, Journal of Magnetism and Magnetic Materials, 518, 167396 (2021).
5. V.　L. Mironov, Generalization of London equations with space-time sedeons, International Journal of Geometric Methods in Modern Physics, 18(3), 2150039 1-10 (2021).
6. V.　L. Mironov, Self-consistent hydrodynamic two-fluid model of vortex plasma, Physics of Fluids, 33(3), 037116 1-8 (2021).
7. V.L. Mironov, D.A.　Tatarskiy, A.D.　Efimov, A.A.　Fraerman, Gyrotropic modes of ferromagnetic resonance in system of two exchange-coupled magnetic vortices, IEEE Transactions on Magnetics, 57(10) 4300906 1-6 (2021).
8. M.V. Sapozhnikov, D.A. Tatarskiy, V.L. Mironov, Creating and detecting a magnetic bimeron by magnetic force microscope probe, Journal of Magnetism and Magnetic Materials, 549, 169043 (2022).
9. D.A. Tatarskiy, V.L. Mironov, E.V. Skorokhodov, A.A. Fraerman, Impact of magnetic resonance force microscope probe on gyrotropic mode of magnetic vortex oscillations, Journal of Magnetism and Magnetic Materials, 552, 169152 (2022).
10. V.L. Mironov, Self-consistent hydrodynamic model of electron vortex fluid in solids, Fluids, 7, 330 (2022).
11. V.L. Mironov, Quaternion equations for hydrodynamic two-fluid model of vortex plasma, International Journal of Geometric Methods in Modern Physics, 20(1) 2350016 (2023).
12. V.L. Mironov, S.V. Mironov, Vortex model of plane Couette flow, Fluids, 8(6), 165 (2023).
13. V.L. Mironov, S.V. Mironov, Scalar fields described by Dirac quaternion wave equation, International Journal of Geometric Methods in Modern Physics, 20(13) 2350227 (2023).
14. D.A. Tatarskiy, A.N. Orlova, E.V. Skorokhodov, I.Yu. Pashenkin, V.L. Mironov, S.A. Gusev, Magnetic vortex states manipulation in overlapping ferromagnetic disks, Journal of Magnetism and Magnetic Materials, 590, 171580 (2024).

Doctor Sergey Mironov is the senior researcher at the Institute for Physics of Microstructures of the Russian Academy of Sciences, PhD. His primary areas of scientific interests include solid state physics and mathematical physics. Recent publications

1. S. Mironov, H. Meng, A. Buzdin, Magnetic flux pumping in superconducting loop containing a Josephson ψ junction, Appl. Phys. Lett. 116, 162601 (2020).
2. S.V. Mironov, A.I. Buzdin, Collective magnetic and plasma excitations in Josephson ψ junctions, Phys. Rev. B, 104, 134502 (2021).
3. S. Mironov, A. Mel’nikov, I. Tokman, V. Vadimov, B. Lounis, A. Buzdin, Inverse Faraday Effect for Superconducting Condensates, Phys. Rev. Lett. 126, 137002 (2021).
4. S. Komori, J. M. Devine-Stoneman, K. Ohnishi, G. Yang, Zh. Devizorova, S. Mironov, X. Montiel, L. A. B. Olde Olthof, L. F. Cohen, H. Kurebayashi, M. G. Blamire, A. I. Buzdin, J. W. A. Robinson, Spin-orbit coupling suppression and singlet-state blocking of spin-triplet Cooper pairs", Sci. Adv. 7, eabe0128 (2021).
5. A.V. Putilov, S.V. Mironov, A.S. Mel'nikov, A.I. Buzdin, Giant electromagnetic proximity effect in superconductor/ferromagnet superlattices, Phys. Rev. B, 105, 064510 (2022).
6. M.D. Croitoru, S.V. Mironov, B. Lounis, and A.I. Buzdin, Toward the Light-Operated Superconducting Devices: Circularly Polarized Radiation Manipulates the Current-Carrying States in Superconducting Rings, Adv. Quantum Technol. 5, 2200054 (2022).
7. A.A. Kopasov, Zh. Devizorova, H. Meng, S.V. Mironov, A.S. Melnikov, A.I. Buzdin, Adiabatic phase pumping in S/F/S hybrids with noncoplanar magnetization, Phys. Rev. B 108, 224511 (2023).
8. A.V. Putilov, S.V. Mironov, A.I. Buzdin, Nonreciprocal electron transport in finitesize superconductor/ferromagnet bilayers with strong spin-orbit coupling, Phys. Rev. B 109, 014510 (2024).