We discuss the fate of the axial U(1) symmetry in 2-flavor QCD at finite temperature, where the non-singlet chiral symmetry is restored. We first summarize the previous theoretical investigation on the relation between the eigenvalue density of the Dirac operator and the axial U(1) symmetry. We show that the eigenvalue density near the origin behaves as λ γ with γ > 2 in the chirally symmetric ...

A phenomenological successful effective chiral theory of pseudoscalar, vector, and axial-vector mesons is introduced. Based on this theory all the 10 coefficients of ChPT are predicted. It has been found that a new symmetry breaking-axial-vector symmetry breaking is responsible for the mass difference between ρ and a1 mesons. It is shown that in an EW theory without Higgs mW and mZ are dynamica...

Normal human brains present an approximate bilateral symmetry. This symmetry is reflected in CT and MR images depicting axial and coronal slices of the brain. Though the internal structure of a pathologic brain may depart from its normal bilateral symmetry, the ideal imaginary bilateral symmetry plane remains invariant. This plane is often referred to as the mid-sagittal plane of the brain. Aut...

The maximally complicated arbitrary-dimensional “maximal” Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D− to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, b...