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Solution of Schwinger-Dyson Equations for ${\cal PT}$-Symmetric Quantum Field Theory

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arxiv hep-th/9907045 v1 pith:I7CHYOYJ submitted 1999-07-07 hep-th

classification hep-th
keywords fieldquantumtheoriestheorydescribingequationspositiveschwinger-dyson
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing $ig\phi^3$ and $-g\phi^4$ field theories, still possess real positive spectra so long as the weaker condition of ${\cal PT}$ symmetry holds. This allows for the possibility of new kinds of quantum field theories that have strange and quite unexpected properties. In this paper a technique based on truncating the Schwinger-Dyson equations is presented for renormalizing and solving such field theories. Using this technique it is argued that a $-g\phi^4$ scalar quantum field theory in four-dimensional space-time is renormalizable, is asymptotically free, has a nonzero value of $<0|\phi|0>$, and has a positive definite spectrum. Such a theory might be useful in describing the Higgs boson.

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 126 citations worldwide. Full citation record

  1. Tensor Network Formulation of $\mathcal{PT}$-Symmetric Quantum Field Theory

    hep-th 2026-08 accept novelty 6.0 of 10

    A tensor network representation of PT-symmetric φ^4 lattices on complex contours yields exact parity-decomposed local tensors and a finite-volume identity between wedge-contour and continued Hermitian partition functi...

  2. Discrete Dyson-Schwinger equations

    math-ph 2026-03 unverdicted novelty 5.0 of 10

    Discrete Dyson-Schwinger equations for scalar fields produce Gaussian solutions in the continuum limit for d ≥ 4, consistent with Aizenman triviality theorems.

  3. Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature

    hep-lat 2025-09 conditional novelty 4.0 of 10

    Configurational temperature from action gradients and Hessians offers a sensitive new correctness diagnostic for complex Langevin simulations, reproducing input temperature to 0.2-3% in 1D PT-symmetric models.

  4. Review of strongly coupled regimes in gravity with Dyson-Schwinger approach

    gr-qc 2026-03 unverdicted novelty 3.0 of 10

    Dyson-Schwinger methods applied to gravity theories produce conformally flat metrics and a sequence of cosmological phase transitions from conformal symmetry breaking that non-minimal scalar couplings can suppress.

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