Two-dimensional light-front ${\varphi }^4$ theory in a symmetric polynomial basis

Abstract

We study the lowest-mass eigenstates of ${\varphi }_{1+1}^4$ theory with both odd and even numbers of constituents. The calculation is carried out as a diagonalization of the light-front Hamiltonian in a Fock-space representation. In each Fock sector a fully symmetric polynomial basis is used to represent the Fock wave function. Convergence is investigated with respect to the number of basis polynomials in each sector and with respect to the number of sectors. The dependence of the spectrum on the coupling strength is used to estimate the critical coupling for the positive-mass-squared case. An apparent discrepancy with equal-time calculations of the critical coupling is resolved by an appropriate mass renormalization.

arXiv comment18 pages, 8 figures, RevTeX 4.1

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• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Monte Carlo determination of the critical coupling in ${\varphi }_2^4$ theory
• RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• New MC determination of the critical coupling in ${\varphi }_2^4$ theory
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• Structure of light front vacuum sector diagrams
• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
• Longitudinal dynamics for mesons on the light cone
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Critical behavior of the 2d scalar theory: resumming the ${\mathrm{N}}^8\mathrm{LO}$ perturbative mass gap
• Light-front ${\varphi }_2^4$ theory with sector-dependent mass
• Tadpoles and vacuum bubbles in light-front quantization
• Light-front versus equal-time quantization in ${\varphi }^4$ theory
• Symmetry breaking in light-front ${\varphi }^4$ theory
• Convergence of the light-front coupled-cluster method in quenched scalar Yukawa theory
• A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime