PT-Symmetric Quantum Electrodynamics

Abstract

The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^{\mu }$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $\varphi$ has a cubic self-interaction of the form $i{\varphi }^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free.

9 pages, no figures, revtex4

References in corpus (1)

• Ghost Busting: PT-Symmetric Interpretation of the Lee Model

Cited by in corpus (35)

• Making Sense of Non-Hermitian Hamiltonians
• Dual PT-Symmetric Quantum Field Theories
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time evolution of non-Hermitian Hamiltonian systems
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
• Relativistic Non-Hermitian Quantum Mechanics
• Non-Hermitian extension of gauge theories and implications for neutrino physics
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• A return to observability near exceptional points in a schematic PT-symmetric model
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Nonunique C operator in PT Quantum Mechanics
• Light neutrino masses from a non-Hermitian Yukawa theory
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Kurt Symanzik - a stable fixed point beyond triviality
• Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
• Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem
• PT phase transition in multidimensional quantum systems
• Overcritical PT-symmetric square well potential in the Dirac equation
• PT-symmetric operators and metastable states of the 1D relativistic oscillators
• PT-Symmetric Quantum Electrodynamics and Unitarity
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Small-$\epsilon$ behavior of the Non-Hermitian PT-Symmetric Hamiltonian $H=p^2+x^2(ix{)}^{\epsilon }$
• Electric conductivity in non-Hermitian holography
• Neutrino mass observables and non-Hermitian version of Type-I seesaw model
• PT-Symmetry Quantum Electrodynamics--PTQED
• Computation and Verification of Spectra for Non-Hermitian Systems
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• On the non-relativistic limit of charge conjugation in QED
• Anisotropic oscillator with pseudo-hermiticity and its noncommutative extension
• Magnetic QED
• A selection rule for transitions in PT-symmetric quantum theory
• Electric-Magnetic Duality in Massless QED?