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Register a new userSupersymmetric content of the Dirac and Duffin-Kemmer-Petiau equations
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Authors
Andrzej Okninski
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We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with some built-in projection operator. This covariant equation can be referred to as supersymmetric since it has bosonic as well as fermionic degrees of freedom.
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In this paper, we study the covariant Duffin-Kemmer-Petiau (DKP) equation in the space-time generated by a cosmic string and we examine the linear interaction of a DKP field with gravitational fields produced by topological defects and thus study the influence of topology on this system. We highlight two classes of solutions defined by the product of the deficit angle with the angular velocity of the rotating frame. We solve the covariant form of DKP equation in an exact analytical manner for node-less and one-node states by means of an appropriate ansatz.
In the present work a transition from the spin-$0$ Duffin-Kemmer-Petiau equation to the Dirac equation is described. This transformation occurs when a crossed field changes into a certain longitudinal field. An experimental setup to carry out the transition is proposed.
We study relation between the Duffin-Kemmer-Petiau algebras and some representations of Tzou algebras. Working in the setting of relativistic wave equations we reduce, via a similarity transformation, five and ten dimensional Duffin-Kemmer-Petiau algebras to three and seven dimensional Tzou algebras, respectively.
The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is quantized after a constraint analysis following Diracs methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Greens functions are obtained through functional methods and the theorys renormalizability is also detailed presented. Next, the radiative corrections for the Greens functions at $alpha $-order are computed; and, as it turns out, an unexpected $m_{P}$-dependent divergence on the DKP sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, a diagrammatic discussion on the photon self-energy and vertex part at $alpha ^{2}$-order are presented, where it is possible to observe contributions from the DKP self-energy function, and then analyse whether or not this novel divergence propagates to higher-order contributions. Lastly, an energy range where the theory is well defined: $m^{2}ll k^{2}<m_{p}^{2}$ was also found by evaluating the effective coupling for the GSDKP.
We investigate the breaking of Lorentz symmetry caused by the inclusion of an external four-vector via a Chern-Simons-like term in the Duffin-Kemmer-Petiau Lagrangian for massless and massive spin-one fields. The resulting equations of motion lead to the appearance of birefringence, where the corresponding photons are split into two propagation modes. We discuss the gauge invariance of the extended Lagrangian. Throughout the paper, we utilize projection operators to reduce the wave-functions to their physical components, and we provide many new properties of these projection operators.
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