Abstract
Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Phys. Rev. D101 014509 (2020), we quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty, even for volumes that are very large by the standards of present-day Euclidean calculations. We then present an improvement strategy, based in the fact that the finite volume has a reduced symmetry. This implies that kinematic points, which yield the same Lorentz invariants, may still be physically distinct in the finite-volume system. As we demonstrate, both numerically and analytically, averaging over such sets can significantly suppress the unwanted volume distortions and improve the extraction of the physical scattering amplitudes.
Highlights
Nonperturbative descriptions lie at the core of a variety of interesting physical systems, ranging from strong electromagnetic fields, to topological effects in condensed matter systems, to the possible metastability and decay of the Standard Model vacuum
We have explored the prospects for extracting physical scattering amplitudes from Minkowski-signature correlation functions, calculated in a periodic one-dimensional spatial volume with extent L
Defining finite-volume estimators for both hadronic and Compton amplitudes, we have shown how the formalism presented in Ref. [54] can be used to describe the finite-L effects in terms of infinite-volume K matrices and related quantities
Summary
Nonperturbative descriptions lie at the core of a variety of interesting physical systems, ranging from strong electromagnetic fields, to topological effects in condensed matter systems, to the possible metastability and decay of the Standard Model vacuum. Neither correlator has an obvious relation to a physical scattering amplitude, due to the discrete set of finite-volume states With this in mind, especially considering the significant investment in developing viable real-time computations, it is important to understand to what extent CML ðt; pÞ gives a more useful prediction as compared to CELðτ; pÞ. The best-established approach, at present, is to numerically determine finite-volume energies EnðLÞ and matrix elements cnðp; LÞ from Euclidean correlators and, by making use of model-independent field-theoretic relations, to map these into physically observable scattering and decay amplitudes. To summarize the results so far, our master equation, Eq (22), gives an expression for the L dependence of T L, in terms of expressions for the infinite-volume amplitudes T , H, H0, and M This provides a tool to explore optimal numerical strategies for approaching the physical amplitude in future Minkowski-signature calculations, especially for nonperturbative systems. E 1⁄4 ωp þ ωq, we recover a nonzero value of MLðE þ iε; PÞ which estimates the amplitude up to corrections of order ðQ2 þ m2Þ 1⁄4 OðεÞ
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