Hypercomplex formulation of dissipative scalar electrodynamics and phase transitions

Abstract

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.