Hamiltonian formulation of the $1+1$-dimensional ${\varphi }^4$ theory in a momentum-space Daubechies wavelet basis

Abstract

We apply the wavelet formalism of quantum field theory to investigate nonperturbative dynamics within the Hamiltonian framework. In particular, we employ Daubechies wavelets in momentum space, whose basis functions are labeled by resolution and translation indices, providing a natural nonperturbative truncation of both infrared and ultraviolet truncation of quantum field theories. As an application, we compute the energy spectra of a free scalar field theory and the interacting $1+1$-dimensional ${\varphi }^4$ theory. This approach successfully reproduces the well-known strong-coupling phase transition in the $m^2>0$ regime. We find that the extracted critical coupling systematically converges toward its established value as the momentum resolution is increased, demonstrating the effectiveness of the wavelet-based Hamiltonian formulation for nonperturbative field-theoretic calculations.

References in corpus (36)

• Nonperturbative Light-Front QCD
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• Matrix product states and variational methods applied to critical quantum field theory
• Entanglement renormalization and wavelets
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• NLO Renormalization in the Hamiltonian Truncation
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• Monte Carlo determination of the critical coupling in ${\varphi }_2^4$ theory
• Truncated Hilbert space approach to the 2d ${\varphi }^4$ theory
• Towards Quantum Simulations in Particle Physics and Beyond on Noisy Intermediate-Scale Quantum Devices
• Wavelets in Field Theory
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Continuous Wavelet Transform in Quantum Field Theory
• New MC determination of the critical coupling in ${\varphi }_2^4$ theory
• Simulation of Field Theories in Wavelet Representation
• A New Formulation and Regularization of Gauge Theories Using a Non-Linear Wavelet Expansion
• Hamiltonian Truncation Effective Theory
• Critical mass renormalization in renormalized phi4 theories in two and three dimensions
• Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory
• Efficient Quantum Algorithm for All Quantum Wavelet Transforms
• Wavelet-Based Quantum Field Theory
• Wavelet-induced renormalization group for the Landau-Ginzburg model
• Multiresolution decomposition of quantum field theories using wavelet bases
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Wavelets and renormalization group in quantum field theory problems
• On quantization in light-cone variables compatible with wavelet transform
• Multi-scale methods in quantum field theory
• Wavelet field decomposition and UV `opaqueness'
• Renormalization in Wavelet basis
• Hamiltonian Flow Equations in Daubechies Wavelet Basis

Cited by in corpus (1)

• An efficient Wavelet-Based Hamiltonian Formulation of Quantum Field Theories using Flow-Equations