Reconstructing propagators of confined particles in the presence of complex singularities,Physical Review D

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Reconstructing propagators of confined particles in the presence of complex singularities
Physical Review D ( IF 4.6 ) Pub Date : 2021-10-20 , DOI: 10.1103/physrevd.104.074024
Yui Hayashi ₁ , Kei-Ichi Kondo _{1,

2}

Affiliation

Propagators of confined particles, especially the Landau-gauge gluon propagator, may have complex singularities as suggested by recent numerical works as well as several theoretical models, e.g., motivated by the Gribov problem. In this paper, we study formal aspects of propagators with complex singularities in reconstructing Minkowski propagators starting from Euclidean propagators by the analytic continuation. We derive the following properties rigorously for propagators with arbitrary complex singularities satisfying some boundedness condition. The two-point Schwinger function with complex singularities violates the reflection positivity. In the presence of complex singularities, while the holomorphy in the usual tube is maintained, the reconstructed Wightman function on the Minkowski spacetime becomes a nontempered distribution and violates the positivity condition. On the other hand, the Lorentz symmetry and locality are kept intact under this reconstruction. Finally, we argue that complex singularities can be realized in a state space with an indefinite metric and correspond to confined states. We also discuss consequences of complex singularities in the Becchi-Rouet-Stora-Tyutin formalism. Our results could open up a new way of understanding a confinement mechanism, mainly in the Landau-gauge Yang-Mills theory.

中文翻译：

在存在复杂奇点的情况下重建受限粒子的传播子

受限粒子的传播子，尤其是朗道规范胶子传播子，可能具有复杂的奇点，正如最近的数值工作以及一些理论模型所暗示的那样，例如，受格里波夫问题的启发。在本文中，我们研究了具有复奇点的传播子的形式方面，以通过解析延拓从欧几里得传播子重建闵可夫斯基传播子。对于具有满足某些有界条件的任意复奇点的传播器，我们严格推导出以下性质。具有复奇点的两点 Schwinger 函数违反了反射正性。在复奇点存在的情况下，在通常的管中保持全纯，Minkowski 时空上重建的 Wightman 函数变为非调和分布，违反了正性条件。另一方面，洛伦兹对称性和局域性在这种重建下保持完整。最后，我们认为复杂奇点可以在具有不确定度量的状态空间中实现并对应于受限状态。我们还讨论了 Becchi-Rouet-Stora-Tyutin 形式主义中复杂奇点的后果。我们的结果可以开辟一种理解限制机制的新方法，主要是在 Landau-gauge Yang-Mills 理论中。我们还讨论了 Becchi-Rouet-Stora-Tyutin 形式主义中复杂奇点的后果。我们的结果可以开辟一种理解限制机制的新方法，主要是在 Landau-gauge Yang-Mills 理论中。我们还讨论了 Becchi-Rouet-Stora-Tyutin 形式主义中复杂奇点的后果。我们的结果可以开辟一种理解限制机制的新方法，主要是在 Landau-gauge Yang-Mills 理论中。

更新日期：2021-10-20

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