Variational method in relativistic quantum field theory without cutoff

Abstract

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the 3 requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.

v2 - major update on the algorithm v1 - 4 pages - see same posting for a longer companion paper "Relativistic continuous matrix product states for quantum fields without cutoff" containing more derivations, context, and explanations

References in corpus (5)

• Continuous Matrix Product States for Quantum Fields
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Relativistic continuous matrix product states for quantum fields without cutoff
• Computing energy density in one dimension

Cited by in corpus (5)

• Relativistic continuous matrix product states for quantum fields without cutoff
• Towards a nonperturbative construction of the $S$-matrix
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Tensor Renormalization Group for interacting quantum fields
• Entanglement Renormalization of the class of Continuous Matrix Product States