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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

PT-symmetric quantum electrodynamics and unitarity.

Kimball A Milton¹, E K Abalo, Prachi Parashar

¹Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019-2061, USA. milton@nhn.ou.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|March 20, 2013

Summary

Parity-time (PT) symmetry offers an alternative to Hermiticity in quantum mechanics. While PT-invariant quantum electrodynamics (QED) shows promise, maintaining unitarity remains a challenge.

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Area of Science:

Theoretical Physics
Quantum Mechanics
Quantum Field Theory

Background:

Hermiticity in quantum mechanics can be replaced by parity-time (PT) symmetry.
PT symmetry ensures positive energies and unitarity in quantum mechanics.
PT-invariant quantum electrodynamics (QED) was proposed as a higher-dimensional extension.

Purpose of the Study:

To review the status of PT-invariant QED.
To examine the general issue of unitarity in PT-symmetric theories.
To address challenges in maintaining unitarity in PT QED.

Main Methods:

Analysis of scattering matrix unitarity.
Examination of Källén spectral representation for photon propagators.
Investigation of Green's functions and analyticity requirements.

Main Results:

Difficulties persist in establishing unitarity in PT-invariant QED.
Questions arise regarding probability conservation in PT-symmetric quantum mechanics.
The physical consistency of PT QED is under scrutiny.

Conclusions:

The maintenance of unitarity in PT-invariant QED is problematic.
Further investigation is needed to confirm probability conservation in PT-symmetric systems.
The viability of PT QED requires rigorous examination of unitarity and physical requirements.