Discrete Dyson-Schwinger equations for scalar fields produce Gaussian solutions in the continuum limit for d ≥ 4, consistent with Aizenman triviality theorems.
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.
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2026 2verdicts
UNVERDICTED 2representative citing papers
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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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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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.