AI 中文总结
研究基于超复数公式发展标量电动力学，通过构建有效自由能泛函推导方程并分析稳定性，确立双临界点存在，揭示越过临界温度时系统经历一阶相变，还表明特定条件下会出现结构不稳定性。
AI 中文摘要
本文发展了标量电动力学的超复数公式，其中耗散作为由扩展局部规范对称性U(1)×SO(1,1)决定的内在动力学性质出现。通过构建有效自由能泛函，推导广义金兹堡 - 朗道方程并分析系统的热力学稳定性。对真空态至四阶的分析表明，与不变量相关系数的约束禁止混合态共存，正式确立双临界点的存在。因此，越过临界温度时，系统被迫经历不连续的一阶相变。此外，还证明当有效四次耦合取负值时，双曲对称会引发结构不稳定性，使自由能无下界并产生渐近不稳定方向。
英文摘要
A hypercomplex formulation of scalar electrodynamics is developed, in which dissipation emerges as an intrinsic dynamic property dictated by the extended local gauge symmetry U(1)XSO(1,1). By constructing an effective free-energy functional, we derive the generalized Ginzburg-Landau equations and analyze the thermodynamic stability of the system. Our analysis of the vacuum state up to the fourth order reveals that the constraint on the coefficients associated with the invariants prohibits the coexistence of mixed states, formally establishing the existence of a bicritical point. Consequently, upon crossing the critical temperature, the system is forced to undergo a discontinuous first-order phase transition. Furthermore, we demonstrate that the hyperbolic symmetry induces a structural instability when the effective quartic couplings take negative values, rendering the free energy unbounded from below and creating asymptotic directions of instability.
Comments21 pages and 5 figures
