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Scalar quantum field theory with a complex cubic interaction.

Carl M Bender1, Dorje C Brody, Hugh F Jones

  • 1Blackett Laboratory, Imperial College, London SW7 2BZ, UK.

Physical Review Letters
|February 9, 2005
PubMed
Summary
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This study demonstrates that a specific quantum field theory is physically valid due to its positive spectrum and unitarity. A novel operator, C, was developed to define the Hilbert space, confirming the theory's acceptability.

Area of Science:

  • Quantum Field Theory
  • Theoretical Physics
  • Mathematical Physics

Background:

  • PT-symmetric quantum field theories offer a framework for studying non-Hermitian systems.
  • Establishing the physical acceptability of quantum field theories requires positive spectra and unitarity.
  • Previous models faced challenges in defining a consistent Hilbert space inner product.

Purpose of the Study:

  • To demonstrate the physical acceptability of an i phi(3) quantum field theory.
  • To introduce a method for defining the Hilbert space inner product in PT-symmetric theories.
  • To establish the existence of a new, time-independent observable.

Main Methods:

  • Perturbative construction of a linear operator C.
  • Analysis of the spectrum for positivity.

Related Experiment Videos

  • Verification of the theory's unitarity.

    • Main Results:

    • The i phi(3) quantum field theory possesses a positive spectrum.
    • The theory is shown to be unitary.
    • A novel, time-independent observable operator C was successfully constructed.

    Conclusions:

    • The i phi(3) quantum field theory is a physically acceptable model.
    • The constructed operator C is crucial for defining the Hilbert space inner product.
    • This work provides a new tool for analyzing PT-symmetric quantum field theories.