耗散量子场论的超复配分函数
A hypercomplex partition function for dissipative quantum field theory
AI总结：
该研究构建超复耗散量子场论的有限温度配分函数，揭示其微扰层级，证明耗散可通过扩展代数热结构编码，为超复方法在相关量子系统的应用开辟了路径。
AI中文摘要：
我们采用虚时路径积分方法与超复代数的幂等结构，构建了超复耗散量子场论[1]的有限温度形式。所得配分函数自然分解为两个共轭复扇区，二者的结合既保留超复厄米结构，又生成非平凡热相。通过该构造可一致得到标准热力学可观测量，且在耗散消失极限下还原为常规相对论带电玻色气体。超出该平衡对应关系，超复形式揭示出独特的微扰层级：耗散效应首先出现在互补相扇区，而对普通实热力学量的修正仅在高阶出现。这些结果表明，耗散可通过扩展的代数热结构编码，无需放弃熟悉的相对论有限温度场论框架，为超复方法在耗散、开放及有效非厄米量子系统中的更广泛应用开辟了路径。
英文摘要：
We develop a finite-temperature formulation for a hypercomplex dissipative quantum field theory [1], using the imaginary-time path-integral approach and the idempotent structure of the hypercomplex algebra. The resulting partition function naturally separates into two conjugate complex sectors whose recombination preserves the hypercomplex Hermitian structure while generating a nontrivial thermal phase. From this construction, the standard thermodynamic observables are obtained consistently, and the conventional relativistic charged Bose gas is recovered in the vanishing-dissipation limit. Beyond this equilibrium correspondence, the hypercomplex formulation reveals a distinctive perturbative hierarchy: dissipative effects first appear in the complementary phase sector, while corrections to ordinary real thermodynamic quantities arise only at higher order. These results show that dissipation can be encoded through an enlarged algebraic thermal structure without abandoning the familiar framework of relativistic finite-temperature field theory, opening a path toward broader applications of hypercomplex methods in dissipative, open, and effectively non-Hermitian quantum systems.
