Integrable dissipative structures in the gauge theory of gravity
L. Martina (1), O.K. Pashaev(2), G. Soliani (1) ((1) Lecce Univ., (Italia), (2) JINR Dubna (Russia))
TL;DR
This paper explores how the gauge formulation of 1+1 dimensional gravity relates gauge fixing conditions to integrable hierarchies, revealing dissipative structures and spontaneous symmetry breaking.
Contribution
It demonstrates that the equations for Zweibein fields can be expressed as reaction-diffusion type evolution equations with dissipative solutions in the gauge theory of gravity.
Findings
Equations for Zweibein fields are reaction-diffusion type
Spectral parameter linked to $SO(1,1)$ gauge symmetry
Discussion of spontaneous symmetry breaking and irreversibility
Abstract
The Jackiw-Teitelboim gauge formulation of the 1+1 dimensional gravity allows us to relate different gauge fixing conditions with integrable hierarchies of evolution equations. We show that the equations for the Zweibein fields can be written as a pair of time reversed evolution equations of the reaction-diffusion type, admitting dissipative solutions. The spectral parameter for the related Lax pair appears as the constant valued spin connection associated with the gauge symmetry. Spontaneous breaking of the non-compact symmetry and the irreversible evolution are discussed.
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