It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be...

Appelquist and Chanowitz have derived an upper bound on the scale of fermion mass generation, proportional to v/mf , by considering the scattering of same-helicity fermions into pairs of longitudinal weak vector bosons in a theory without a standard Higgs boson. We show that the derivation of this bound is based on an inconsistent set of assumptions. We argue that there is no upper bound on the...

In various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1+8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly,...

Using a simple model, a new sphaleron solution which incorporates finite fermionic density effects is obtained. The main result is that the height of the potential barrier (sphaleron energy) decreases as the fermion density increases. This suggests that the rate of sphaleron-induced transitions increases when the fermionic density increases. However the rate increase is not expected to change s...

The anomaly for the fermion number current is calculated on the lattice in a simple prototype model with an even number of fermion doublets.

We show that the spontaneous magnetization occurs as realization of finite density vacua, those are the lowest Landau levels fully or half occupied by fermions, in (2+1)-dimensional QED with a Chern-Simons term. The charge condensation is shown to appear so as to complement the fermion anti-fermion condensate which breaks the flavor U(2N) symmetry and causes the fermion mass generation. The sol...

We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number 〈N〉 is a thermal expectation value, and we compute the finite temperature fluctuations, (∆N) = 〈N〉 − 〈N〉. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopologica...

Renormalization of a lattice chiral fermion due to the exchange of the non-Abelian gauge bosons is studied in the overlap formulation at one loop level. Divergent terms breaking the chiral symmetry do not appear and a chiral fermion is renormalized, preserving the correct chiral properties without adding new counter-terms or tuning the parameters involved. The divergent part of the wave functio...

We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered 8-vertex model. Using this equivalence we deduce the solution of the odd 8-vertex ...

During the last few years, investigations of rare-earth materials have made clear that heavy fermion quantum criticality exhibits novel physics not fully understood. In this work, we write for the first time the effective action describing the low energy physics of the system. The f fermions are replaced by a dynamical scalar field whose nonzero expected value corresponds to the heavy fermion p...