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A Variational Approach to Quantum Field Theory
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In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which provides variational upper bounds on the energy eigenstates of the theory. An essential step in the variational method is the choice of trial wave function. In this work, we study the viability of employing a neural network as our variational ansatz. As a first step towards phenomenologically interesting strongly coupled theories like quantum chromodynamics, we study scalar field theories with quartic couplings.
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Cited by 3 Pith papers
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Neural Wavefunctions in Quantum Field Theory I: Asymptotic Freedom
Neural network wavefunctions enable variational calculations that reproduce asymptotic freedom, dynamical mass generation, and step-scaling in the 2D nonlinear sigma model.
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Neural Wavefunctions in Quantum Field Theory I: Asymptotic Freedom
Neural-network wavefunctions enable variational Monte Carlo calculations that reproduce asymptotic freedom, dynamical mass generation, and the step-scaling function in the 2D nonlinear sigma-model.
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Variational Neural Network Approach to QFT in the Field Basis
A variational neural network ansatz approximates the ground-state wavefunctional of the free Klein-Gordon theory in momentum-space field basis and is validated against exact analytic observables.
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