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We show that, contrary to previous belief, even in models with chiral fermions coupled to a dynamical gauge field an improved quantization procedure leads to a quantum system which is gauge (BRST) invariant; there are no genuine anomalies which spoil this invariance. This statement is proven in the path integral formalism for the general case, and is made explicit for the chiral Schwinger model, which leads to a consistent quantum theory in spite of the “anomaly”.

We investigate the effects of temperature in the instanton description of the QCD vacuum with light quarks. Using variational arguments, a mean-field approximation and a semiquenched fermion determinant, we find a chiral phase transition for more than one massless flavor. Results for the chiral condensate and the constituent mass are presented.

It is usually believed that unlike the external magnetic field which one can set directly, vorticity is a property of the flow of particles, which is indirectly controlled by external fields and initial conditions. Using the curved-space technics it is shown that the influence of the vorticity on the relativistic chiral fermions can indeed be controlled directly., Comment: 21 pages, 1 figure

We show from first principles, using explicitly invariant Pauli-Villars regularization of chiral fermions, that the Nieh-Yan form does contribute to the Adler-Bell-Jackiw (ABJ) anomaly for spacetimes with generic torsion, and comment on some of the implications. There are a number of interesting and important differences with the usual ABJ contributions in the absence of torsion. For dimensional reasons, the Nieh-Yan contribution is proportional to the square of the regulator mass. In spacetimes with flat vierbein but non-trivial torsion, the associated diagrams are actually vacuum polarization rather than triangle diagrams, and the Nieh-Yan contribution to the ABJ anomaly arises from the fact that the axial torsion "photon" is not transverse., Comment: 9 pages, replaced with revtex file

Neville's construction of fermions with chiral asymmetry in the presence of torsion on ${S}^{4}$ is generalized to the case of ${S}^{4p}$. It is pointed out that in all cases pg1 the tangent group is SO(4p), while for p=1 it is SU(2).