Description
Quantum tunnelling of a particle through a potential barrier, while widely understood in quantum mechanics, has yet to receive a systematic treatment in quantum field theory for particles coupled to an external background. We aim to determine QFT corrections to barrier tunnelling, which requires resummation of Feynman diagrams to all orders, as this interaction is non-perturbative in the potential.
Preliminary works by Zielinski et al. [1,2] focused on scalar theories, and [2] remains open due to computational intractability. Recent progress by Fleming [3] with spinor fields utilised Dirac algebra and certain approximations to obtain a system of ODEs which solve for the transmission and reflection amplitudes for static $1$D potentials.
We present a self-consistent diagrammatic approach through three-point couplings to the background (including vertex corrections), which yields the field-theoretic generalisation, for any spin and allowable tensor background structure, of the Lippmann-Schwinger equations in quantum mechanics. For static $1$D potentials, under certain approximations to the dressed propagator and vertex functions, this can be reduced to a system of ODEs for the propagated $T$-matrix in position space. This unified framework can help us understand the extent of quantum corrections in phenomena such as $\alpha$-decay, deep sub-barrier fusion, and $2$-proton radioactivity, through theories like scalar QED and QED.
Preliminary calculations using an interacting scalar theory $A\phi^2$ with a mediator mass $m_A=m_\phi/2$ and a Dirac-delta potential show $\sim 1$% reduction in transmission compared to RQM at one-loop order, for unit dimensionless coupling. Next, we aim to extend this approach to scalar QED and include multi-particle final states to explore $\alpha$-decay, and address long-standing questions, including the effect of Bremsstrahlung during tunnelling [4] and tunnelling times.
[1] Eur.Phys.J.C 84,992 (2024). [2] Eur.Phys.J.C 84,967 (2024). [3] M. Fleming, “Non-Perturbative Spinor Tunnelling in Interacting Quantum Fields”, Honours Thesis (Australian National University, 2025). [4] Phys.Rev.C 89,014602 (2014).
| I am the presenting author | Yes |
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