Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory

Quantization of Dirac Field

Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries

We study space-time symmetries in scalar quantum field theory on an arbitrary static space-time. We first consider Euclidean quantum field theory, and show that the isometry group is generated by one-parameter subgroups which have either selfadjoint or unitary quantizations. We then show that the self-adjoint semigroups thus constructed can be analytically continued to one-parameter unitary gro...

Microcausality of Dirac field on noncommutative spacetime

We study the microcausality of free Dirac field on noncommutative spacetime. We calculate the vacuum and non-vacuum state expectation values for the Moyal commutator [ψα(x) ⋆ ψβ(x), ψσ(x ) ⋆ ψτ (x )]⋆ of Dirac field on noncommutative spacetime. We find that they do not vanish for some cases of the indexes for an arbitrary spacelike interval, no matter whether θ = 0 or θ 6= 0. However for the ph...

covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the...

Anticommutators and propagators of Moyal star-products for Dirac field on noncommutative spacetime

We study the Moyal anticommutators and their expectation values between vacuum states and non-vacuum states for Dirac fields on noncommutative spacetime. Then we construct the propagators of Moyal star-products for Dirac fields on noncommutative spacetime. We find that the propagators of Moyal star-products for Dirac fields are equal to the propagators of Dirac fields on ordinary commutative sp...