Abstract The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time (T), flips spatial parity (P), and conjugates charge (C). Although its physical basis remains obscure, CPT symmetry appears to be necessary in order to unify quantum mechanics with relativity. This paper attempts to decipher the physical reasoning behind proofs of the CPT theorem in algebraic quantum field theory. Ultimately, CPT symmetry is linked to a reversal of the C * -algebraic Lie product that encodes the generating relationship between observables and symmetries. In any physically reasonable relativistic quantum field theory, it is always possible to systematically flip this generating relationship while preserving the dynamics, spectra, and localization properties of physical systems. Rather than the product of three separate reflections, CPT symmetry is revealed to be a single global reflection of the theory's state space.

中文翻译：

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解释代数CPT定理

摘要CPT定理指出，任何因果关系，洛仑兹不变量，热力学行为良好的量子场论在反射对称性下也必须是不变的，该对称性可逆转时间方向（T），翻转空间奇偶性（P）和共轭电荷（C ）。尽管其物理基础仍然晦涩难懂，但CPT对称性似乎是必要的，以便使相对论统一量子力学。本文试图解释代数量子场论中CPT定理证明背后的物理推理。最终，CPT对称性与C *-代数Lie乘积的逆向相关，该乘积编码可观察值和对称性之间的生成关系。在任何物理上合理的相对论量子场论中，总是有可能系统地翻转这种生成关系，同时保留动力学，光谱，和物理系统的本地化属性。CPT对称性不是三个独立反射的乘积，而是被揭示为该理论状态空间的单个全局反射。