Constrained symplectic quantization applied to the free scalar field reproduces the Feynman generating functional in the continuum limit and matches standard correlators, commutators, and Dyson-Schwinger equations in 1+1 dimensions via numerical evolution.
The Lefschetz thimble and the sign problem
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abstract
In this talk I review the proposal to formulate quantum field theories (QFTs) on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations of lattice QFTs affected by sign problem. First I will review the theoretical justification of the approach, and comment on some open issues. Then, I will review the algorithms that have been proposed and are being tested to represent and simulate a lattice QFT on a Lefschetz thimble. In particular, I will review the lessons from the very first models of QFTs that have been studied with this approach.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Constrained symplectic quantization recovers the Feynman generating functional with correct real-time prescription for relativistic QFT by analytic continuation of fields and action plus constraints on stable trajectories, tested via two-point functions and Dyson-Schwinger identities on a free scala
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Constrained Symplectic Quantization II: The Free Scalar Field
Constrained symplectic quantization applied to the free scalar field reproduces the Feynman generating functional in the continuum limit and matches standard correlators, commutators, and Dyson-Schwinger equations in 1+1 dimensions via numerical evolution.
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Constrained Symplectic Quantization: Disclosing the Deterministic Framework Behind Quantum Field Theory
Constrained symplectic quantization recovers the Feynman generating functional with correct real-time prescription for relativistic QFT by analytic continuation of fields and action plus constraints on stable trajectories, tested via two-point functions and Dyson-Schwinger identities on a free scala