2020/03/31 by E. Harikumar, Vishnu Rajagopal
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Canonical quantization #Conservation law #Conserved quantity #Dirac algebra #Dirac equation #Dirac operator #Dirac spinor #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #Spinor #Two-body Dirac equations #hep-th
paper · pdf · doi:10.1142/s0217751x2050147x
published as International Journal of Modern Physics A Vol. 35 (2020) 2050147 · 18 page, More discussions, calculations and references added
openalex created_date 2020/03/06 · arxiv created 2020/06/03 · openalex publication_date 2020/09/01 · arxiv updated 2020/12/24 · openalex updated_date 2026/08/05
In this paper, we study the quantization of Dirac field theory in the [Formula: see text]-deformed space–time. We adopt a quantization method that uses only equations of motion for quantizing the field. Starting from [Formula: see text]-deformed Dirac equation, valid up to first order in the deformation parameter [Formula: see text], we derive deformed unequal time anticommutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anticommutation relations between [Formula: see text]-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the [Formula: see text]-deformed conserved currents, valid up to first order in [Formula: see text], corresponding to parity and time-reversal symmetries of [Formula: see text]-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in [Formula: see text]. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its antiparticle satisfy different equations in [Formula: see text] space–time.