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1. Quark Condensate

   Linked via "quark flavors"

   Theoretical Framework and Vacuum Energy
   In the idealized limit of massless quarks, the QCD Lagrangian possesses an exact chiral symmetry, represented by the group $SU(Nf)L \times SU(Nf)R$, where $N_f$ is the number of active light quark flavors (typically $u$, $d$, and $s$). The measured physical masses of hadrons, particularly the light pseudoscalar mesons (pions ( $\pi^\pm$, $\pi^0$), kaons), strongly suggest …

2. Quark Condensate

   Linked via "quark flavors"

   Temperature Dependence
   As the temperature of strongly interacting matter increases, the thermal fluctuations begin to dominate the quantum vacuum state's structure. Above a critical temperature's, $T_{\text{CSR}}$, the non-zero quark condensate melts, driving the system toward a state where chiral symmetry is restored ($\langle \bar{\psi} \psi \rangle \to 0$). This transition is generally modeled as a smooth, crossover phenomenon for light [quark …