Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors
AbstractA new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis of Grassmann variables, which we call gamma operators. Various field theory constructions are defined with use of these structures. We derive formulas for the vacuum state vector. Five operator analogs of five Dirac gamma matrices exist in the superalgebraic approach as well as two additional operator analogs of gamma matrices, which are absent in the theory of Dirac spinors. We prove that there is a relationship between gamma operators and the most important physical operators of the second quantization method: number of particles, energy–momentum and electric charge operators. In addition to them, a series of similar operators are constructed from the creation and annihilation operators, which are Lorentz-invariant analogs of Dirac matrices. However, their physical meaning is not yet clear. We prove that the condition for the existence of spinor vacuum imposes restrictions on possible variants of the signature of the four-dimensional spacetime. It can only be (1,
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Monakhov, V. Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors. Universe 2019, 5, 162.
Monakhov V. Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors. Universe. 2019; 5(7):162.Chicago/Turabian Style
Monakhov, Vadim. 2019. "Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors." Universe 5, no. 7: 162.
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