22-4 Valeriy V. Dvoeglazov

A Note on Constructions of Quantum-Field Operators (414K, PDF) Jan 14, 22

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Abstract. We show some tune points in constructions of field operators in quantum field theory (QFT). They are related to the old discussions on interpretations of the negative-energy solutions of relativistic equations. It is easy to check that both algebraic equation Det( p − m) = 0 and Det( p + m) = 0 for u− and v− 4-spinors have solutions with p0 = Ep = p p2 + m2. The same is true for higher-spin equations. Meanwhile, every book considers the equality p0 = Ep for both u− and v− spinors of the (1/2, 0) ⊕ (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.

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