Extended Equations For Particles – Alina V Ivashkevich

, . ∣ −iiϵJm(z) −i√ϵ2−k2 √2 Jm−1(z) iikJm(z) −i√ϵ2−k2 √2 Jm+1(z) −√2√ϵ2−k2 ϵ Jm−1(z) i k ϵ Jm(z) iJm(z) ∣∣ k ϵ Jm−1(z) i √ϵ2−k2 √2ϵ Jm(z) Jm−1(z) ∣ h0(z) = Jm(z)[ √2a1ϵ2 √ϵ2 −k2 + √2a2kϵ √ϵ2 −k2 + a3ϵ], h1(z) = Jm−1(z)[−ia3√ϵ2 −k2 √2 −ia2k −ia1ϵ], h2(z) = Jm(z)[−√2a2k2 √ϵ2 −k2 −√2a1kϵ √ϵ2 −k2 −a3k], h3(z) = Jm+1(z)[−ia3√ϵ2 −k2 √2 −ia2k −ia1ϵ], E1(z) = Jm−1(z)[− √2a3√ϵ2 −k2 ϵ −a2k ϵ + a4k ϵ −a1], E2(z) = Jm(z)[ i√2a1k √ϵ2 −k2 + ia2(k2 + ϵ2) √2ϵ√ϵ2 −k2 + ia4√ϵ2 −k2 √2ϵ + ia3k ϵ ], E3(z) = −a1Jm+1(z), B1(z) = −a2Jm+1(z), B2(z) = ia3Jm(z), B3(z) = a4Jm−1(z); Below it is convenient to use the shortening notations Jm−1 = J1, Jm = J2, Jm+1 = J3; so we can re-write the known formulas for Bessel functions differently (10.30) 10.4 The Energy-Momentum Tensor In order to separate the gauge solutions and physically observable solutions, we should specify the structure of the energy-momentum tensor for the massless field.

To this end, we should define the relevant matrix of the bilinear form η, which obeys the following restriction (10.31) the explicit form of this matrix is Let us start with an auxiliary tensor Ra b, defined by the formula Ra b(x) = Φ+ηΓa∂bΦ −δa bΨ+ηPΨ that is ( d dz + m z )Jm = +Jm−1 ⟹ d dz J2 = −m z J2 + J1, ( d dz −m z )Jm = −Jm+1 ⟹ d dz J2 = + m z J2 −J3, ( d dz + m + 1 z )Jm+1 = +Jm ⟹ d dz J3 = −m + 1 z ( d dz −m −1 z )Jm−1 = −Jm ⟹ d dz J1 = + m −1 z h−1(Γa)+η = Γa ⟹ ~Γaη = ηΓa, η = ; ∣ ∣ η = .

∣ ∣∣ 0 −1 −1 −1 ∣∣ 1 0 0 0 1 0 0 0 1 0 0 0 −1 0 0 0 −1 0 0 0 −1 ∣ = ∂b −δa bH + ∣ ∣ ∣ K a La ∣ ∣ Ra b(x) = +H + 1 BK a∂bH2 + H + 2 DLa∂bH1 −δa bH + (10.32) Because the above solutions were constructed in cyclic basis, we should transform the right- hand side of relation (10.32) to the same basis.

Extended Equations for Particles Extended Equations for Particles: Spin, General Theory and Exact Solution presents a unified theoretical framework for understanding relativistic wave equations describing particles with spins S = 0, 1/2, 1 and additional internal electromagnetic structure. Through mathematical analysis and physical interpretation, the book bridges fundamental concepts across quantum field theory, relativistic quantum mechanics, and electromagnetic theory.

The text introduces methodologies for developing new relativistic systems of equations that describe particles with electromagnetic characteristics beyond electric charge. Readers will find detailed examinations of the Dirac-Kähler particle and Stueckelberg particle in various external field configurations, including Coulomb, uniform magnetic, and electric fields. Designed as both a reference for researchers and a pedagogical resource for advanced undergraduate and graduate students, this book provides a mathematically rigorous yet accessible treatment of complex theoretical physics concepts.

The unified methodological approach presented throughout makes this a useful contribution to the field of relativistic quantum theory. Key Features: Develops an innovative approach that connects quantum field theory, relativistic quantum mechanics, and electromagnetic theory Makes complex interdisciplinary concepts accessible while maintaining the mathematical rigor essential for advanced research Serves as a cutting-edge reference for active researchers and an accessible pedagogical resource for advanced students Alina V. Ivashkevich is a Researcher at the B.I. Stepanov Istitute of Physics, National Academy of Sciences of Belarus, Department of Fundamental Interactions and Astrophysics.

Elena M. Ovsiyuk is the chair of the Department of Theoretical Physics and Applied Informatics at Mozyr State Pedagogical University, Belarus. Anton V. Bury is a Researcher at the B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Department of Fundamental Interactions and Astrophysics. Aleksander V. Chichurin is a Professor in the Department of Mathematical Modeling, Institute of Mathematics, Informatics and Landscape Architecture, The John Paul II Catholic University of Lublin, Poland.

Vasily V. Kisel is a Researcher at the Department of Theoretical Physics and Applied Informatics, Mozyr State Pedagogical University, Belarus. Viktor M. Red’kov is a Professor and chief Researcher at the B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Department of Fundamental Interactions and Astrophysics. OceanofPDF.com Extended Equations for Particles Spin, General Theory and Exact Solution Alina V.

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

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