5. Theoretical Physics (CSN4)
# Vacuum realization of symmetries from first principles: The Probability Distribution Function formalism

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Auletta A-1 (LNF)
### Auletta A-1

#### LNF

Description

The Probability Distribution Function (p.d.f.) formalism can be used to cast some light on the old aim of understanding the realization of symmetries of QCD from first principles. Applying the p.d.f. to the Wilson regularization, we can explore certain, somewhat overlooked, properties of the Aoki phase. In fact, the p.d.f. states that, either the fermionic bilinear iy¯ g5y can take non-zero values in the Aoki phase, extending thus the current picture of the phase diagram, or there exists an infinite tower of sum-rules the eigenvalues of the Dirac-Wilson operator must comply with. So far, no theoretical argument is strong enough to prove one of these scenarios to be right, thus a dynamical fermion simulation is mandatory at this point.
But the most interesting conclusions appear when we apply the p.d.f. formalism to the Ginsparg-Wilson regularization. There, we see how parity and vector-like symmetries must be realized for a non-vanishing fermion mass.