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- W1488446043 abstract "The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects of modes near zero virtuality. Above T_c, where chiral symmetry is restored, it is shown on general grounds that (in the massless quark limit), the density of states vanishes at zero virtuality faster than $lambda$, where $lambda$ is the virtuality-- $rho(lambda) sim |lambda|^alpha$ is not possible for $alpha le 1$. Isospin invariance is used to show that $rho(lambda) sim m_q^{1-alpha} |lambda|^alpha$ is also not possible for $alpha le 1$. State-of-the-art lattice calculations are reviewed in light of these constraints. In particular, it is argued that violations of these constraints by lattice calculations indicate possible large systematic errors; this raises questions about $U(1)_A$ violating effects seen on the lattice.It is also shown that above $T_c$, the Dirac spectrum has a gap near zero (in the $m_q to 0$ limit) unless contributions from quark-line-connected and disconnected contributions conspire to cancel." @default.
- W1488446043 created "2016-06-24" @default.
- W1488446043 creator A5020982304 @default.
- W1488446043 date "1998-01-28" @default.
- W1488446043 modified "2023-09-27" @default.
- W1488446043 title "The Spectral Density of the Dirac Operator above T_c" @default.
- W1488446043 hasPublicationYear "1998" @default.
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