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Solution of Schwinger-Dyson Equations for ${\cal PT}$-Symmetric Quantum Field Theory
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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.
Forward citations
Cited by 4 Pith papers
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Tensor Network Formulation of $\mathcal{PT}$-Symmetric Quantum Field Theory
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...
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Discrete Dyson-Schwinger equations
Discrete Dyson-Schwinger equations for scalar fields produce Gaussian solutions in the continuum limit for d ≥ 4, consistent with Aizenman triviality theorems.
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Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature
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.
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Review of strongly coupled regimes in gravity with Dyson-Schwinger approach
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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