Classical Physics and Quantum Loops

TL;DR

The paper challenges the common view that the loop expansion in quantum field theory is equivalent to an $\\hbar$-expansion by showing that one-loop diagrams can produce classical contributions when massless propagators are present. Through explicit calculations in QED, gravity, and polarizability systems, it demonstrates that classical terms arise from square-root nonanalyticities in momentum space, while quantum pieces appear as logarithmic corrections, establishing a mixed classical/quantum structure at one loop. A dispersive analysis using Cutkosky rules reveals that the classical effects stem from infrared on-shell regions involving massless exchanges. Collectively, the work argues that the conventional loop-$\\hbar$ correspondence is not generally valid and highlights the infrared origin of classical long-range effects in field theories and quantum gravity.

Abstract

The standard picture of the loop expansion associates a factor of h-bar with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss examples wherein classical effects arise from loop contributions and display the relationship between the classical terms and the long range effects of massless particles.

Figures (3)

• Figure 1: Feynman diagrams for spin 0 radiative corrections to $T_{\mu\nu}$.
• Figure 2: One loop diagrams used to model the interaction of a charged particle with a neutral polarizable system.
• Figure 3: Generic triangle diagram used in dispersive analysis.