ORAL

SESSION: MathematicsWedPM-R3	2nd Intl. Symp. on Sustainable Mathematics Applications
Wed Oct, 25 2017	Room: Peninsula 1
Session Chairs: Zbigniew Oziewicz; Valeriy Dvoeglazov; Session Monitor: TBA

14:30: [MathematicsWedPM05]
The Feynman-Dyson Propagators for Neutral Particles (Local or Non-local?)
Valeriy Dvoeglazov¹ ; ¹Universidad de Zacatecas, Zacatecas, Mexico;
Paper Id: 35 [Abstract]

An analog of the $S=1/2$ Feynman-Dyson propagator is presented in the framework of the $S=1$ Weinberg's theory.The basis for this construction is the concept of the Weinberg field as a system of four field functions differing by parity and by dual transformations. Next, we analyze the recent controversy in the definitions of the Feynman-Dyson propagator for the field operator containing the $S=1/2$ self/anti-self charge conjugate states in the papers by D. Ahluwalia et al. and by W. Rodrigues Jr. et al. The solution of this mathematical controversy is obvious. It is related to the necessary doubling of the Fock Space (as in the Barut and Ziino works), thus extending the corresponding Clifford Algebra. However, the logical interrelations of different mathematical foundations with the physical interpretations are not so obvious (Physics should choose only one correct formalism - it is not clear, why two correct mathematical formalisms (which are based on the same postulates) lead to different physical results.)

SESSION: MathematicsWedAM-R3	2nd Intl. Symp. on Sustainable Mathematics Applications
Wed Oct, 25 2017	Room: Peninsula 1
Session Chairs: Peter Rowlands; Dean Vucinic; Session Monitor: TBA

15:00: [MathematicsWedAM06]
On the Negative-Energy 4-Spinors and Masses in the Dirac Equation
Valeriy Dvoeglazov¹ ; ¹Universidad de Zacatecas, Zacatecas, Mexico;
Paper Id: 36 [Abstract]

It is easy to check that both algebraic equation $Det (\hat p - m) =0$ and $Det (\hat p + m) =0$ for $u-$ and $v-$ 4-spinors have solutions with $p_0= \pm E_p =\pm \sqrt{{\bf p}^2 +m^2}$. The same is true for higher-spin equations. Meanwhile, every book considers the equality $p_0=E_p$ for both $u-$ and $v-$ spinors of the $(1/2,0)\oplus (0,1/2))$ representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both $s=1/2$ and higher spin particles.