Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory

Abstract

We use the interpolating coordinates studied by Hornbostel to investigate a transition from equal-time quantization to light-front quantization, in the context of two-dimensional ${\varphi }^4$ theory. A consistent treatment is found to require careful consideration of vacuum bubbles, in a nonperturbative extension of the analysis by Collins. Numerical calculations of the spectrum at fixed box size are shown to yield results equivalent to those of equal-time quantization, except when the interpolating coordinates are pressed toward the light-front limit. In that regime, a fixed box size is inconsistent with an accurate representation of vacuum-bubble contributions and causes a spurious divergence in the spectrum. The light-front limit instead requires the continuum momentum-space limit of infinite box size. The calculation of the vacuum energy density is then shown to be independent of the interpolation parameter, which implies that the light-front limit yields the same spectrum as an equal-time calculation. This emphasizes the importance of zero modes and near-zero modes in a light-front analysis of any theory with nontrivial vacuum structure.

20 pages, 9 figures, RevTeX 4.1; major revision to include new analysis of vacuum bubble contributions

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Cited by in corpus (6)

• Revealing the structure of light pseudoscalar mesons at the Electron-Ion Collider
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Critical behavior of the 2d scalar theory: resumming the ${\mathrm{N}}^8\mathrm{LO}$ perturbative mass gap
• Tadpoles and vacuum bubbles in light-front quantization
• Multiresolution quantum field theory in light-front coordinates
• Interpolating 't Hooft model between instant and front forms