  Unconventional symmetry breaking due to nonlocal order parameters has
attracted considerable attention in many strongly correlated metals. Famous
examples are the nematic order in Fe-based superconductors and the
star-of-David charge density order in kagome metals. Such exotic symmetry
breaking in metals is a central issue of modern condensed matter physics, while
its theoretical foundation is still unclear in comparison with the
well-established theory of superconductivity. To overcome this difficulty, here
we introduce the "form factor" that generalizes the nonlocal order parameter
into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous
formalism of the "density-wave equation" that gives the thermodynamically
stable form factor, similarly to the superconducting-gap equation. In addition,
a rigorous expression of the Ginzburg-Landau free-energy for the unconventional
order is presented to calculate various thermodynamic properties. In the next
stage, we apply the derived formalism to a typical Fe-based superconductor
FeSe, by using the one-loop LW function that represents the free-energy gain
due to the interference among paramagnons. The following key experiments are
naturally explained: (i) Lifshitz transition (=disappearance of an
electron-pocket) due to the bond+orbital order below $T_c$. (ii) Curie-Weiss
behavior of the nematic susceptibility at higher T, and the deviation from the
Curie-Weiss behavior at lower T near the nematic quantum-critical-point. (iii)
Scaling relation of the specific heat jump at $T_c$, $\Delta C/T_c \propto
T_c^b$ with $b \sim 3$. (Note that b=0 in the BCS theory.) These results lead
to a conclusion that the nematicity in FeSe is the bond+orbital order due to
the "paramagnon interference mechanism". The present theory paves the way for
solving various unconventional phase transition systems.
