Large-momentum convergence of Hamiltonian bound-state dynamics of effective fermions in quantum field theory

TL;DR

This paper compares two approaches to fermion bound-state dynamics in quantum field theory, showing that effective fermions derived via renormalization group methods are less affected by large-momentum divergences than bare fermion approaches.

Contribution

It demonstrates how effective fermions from a renormalization group approach mitigate large-momentum divergences in bound-state calculations compared to traditional bare fermion methods.

Findings

Large-momentum divergences cause buildup of overlapping divergences in bare approaches.

Effective fermion dynamics are minimally affected by large-momentum regions.

Numerical estimates show reduced divergence effects for couplings relevant to quarks.

Abstract

Contributions to the bound-state dynamics of fermions in local quantum field theory from the region of large relative momenta of the constituent particles, are studied and compared in two different approaches. The first approach is conventionally developed in terms of bare fermions, a Tamm-Dancoff truncation on the particle number, and a momentum-space cutoff that requires counterterms in the Fock-space Hamiltonian. The second approach to the same theory deals with bound states of effective fermions, the latter being derived from a suitable renormalization group procedure. An example of two-fermion bound states in Yukawa theory, quantized in the light-front form of dynamics, is discussed in detail. The large-momentum region leads to a buildup of overlapping divergences in the bare Tamm-Dancoff approach, while the effective two-fermion dynamics is little influenced by the large-momentum region. This is illustrated by numerical estimates of the large-momentum contributions for coupling constants on the order of between 0.01 and 1, which is relevant for quarks.