共变虚超光子是否可行？
Is a covariant virtual tachyon viable?
AI总结：
本文探讨纯虚超光子在假子框架内是否可行，发现其违反相对论和量子力学基本原理，排除了共变量子场论中相互作用虚超光子的可能性。
摘要：
Sidney Coleman指出超光子或观察者根据亚光速观察者会能回到时间且轨迹不明确，而不违反洛伦兹不变性[1]。Dragan和Ekert进一步发展了类似思想，提出“量子相对性原理”将两个理论紧密联系[2]。然而，描述为标量场ϕ的本征超光子场理论导致相对论或量子力学基本原理的违反。本文研究纯虚超光子在假子框架内是否一致。我们发现两个致命障碍：首先，洛伦兹 boosts混合产生和湮灭算符，使规范交换关系非不变，尽管真空形式不变。其次，超光子费曼传播子和惠勒传播子的实部支持不重叠，阻止应用假子预设和惠勒-费曼吸收机制。与稳定标准模型场的相互作用进一步违反洛伦兹不变性和等效原理，我们提供了耦合强度的定量限制。我们的分析排除了构建相互作用虚超光子的共变量子场论的可能性。
英文摘要：
Sidney Coleman has noted that superluminal particles or observers would be able to go back in time and have no definite trajectory according to subluminal observers, while not violating Lorentz invariance [1]. Recently, Dragan and Ekert have significantly developed similar ideas even further, which lead to formulation of ``quantum principle of relativity'' that intimately links the two theories [2]. However, field theory descriptions of an on-shell tachyon, described by scalar field $ϕ$ with negative mass squared parameter, lead to violation of basic principles of relativity or quantum mechanics. In this work, we investigate whether purely virtual tachyons can be consistent within the fakeon framework--the only known viable formulation of purely virtual particles. We show that the supports of the real part of the tachyon Feynman propagator, which is also the principal-value propagator (PVP), and the Wheeler propagator intersect only on the light cone. We show that PVP cannot be time-ordered two-point function of a local Hermitian field, excluding the direct extension of the canonical formalism to free fakeon tachyon. Finally, with an imposed tachyonic PVP, interactions with electrons generate composition-dependent accelerations that violate the weak equivalence principle, and we provide a quantitative bound on this scenario. Our analysis identifies obstacles to formulating covariant quantum field theory of interacting virtual tachyon.
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