Dirac and Higher-Spin Equations of Negative Energies
Year: 2011
Type: preprint
Abstract: It is easy to check that both algebraic equation Det(p ̂ − m) = 0 and Det(p ̂ + m) = 0 for 4-spinors u − and v − have solutions with p0 = ±Ep = ± p2 +m2. The same is true for higher-spin equations. Meanwhile, every book considers the p0 = Ep only for both u − and v − spinors of the (1/2, 0)⊕(0, 1/2)) representation, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of negative-energy solutions. Recent works of Ziino (and, independently, 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 spins particles. 1 The Dirac equation is: [iγµ∂µ −m]Ψ(x) = 0. (1) At least, 3 methods of its derivation exist [1, 2, 3]: • the Dirac one (the Hamiltonian should be linear in ∂/∂xi, and be compatible with E2p − p2c2 = m2c4); • the Sakurai one (based on the equation (Ep − σ · p)(Ep + σ · p)φ = m2φ); • the Ryder one (the relation between 2-spinors at rest is φR(0) = ±φL(0)). The γµ are the Clifford algebra matrices γµγν + γνγµ = 2gµν. (2) Usually, everybody uses the following definition of the field operator [4]: Ψ(x) = 1
Source: arXiv (Cornell University)
Author: Valeriy V. Dvoeglazov
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1486758648