Related papers: Axial anomaly and the triality symmetry of octonio…
A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic…
Imposing the conservation equation of the vector current for a fermion of spin $\frac{1}{2}$ at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial--vector fields in six--dimensional curved space is…
We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current satisfies on the classical level a relation that is…
We show that Weyl semimetals exhibit a mixed axial-torsional anomaly in the presence of axial torsion, a concept exclusive of these materials with no known natural fundamental interpretation in terms of the geometry of spacetime. This…
With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse…
We apply the supersymmetric model of \'E. Cartan to the pseudoscalar meson decay into two photons, $\pi_0\to\gamma\gamma$, $\eta\to\gamma\gamma$ and $\eta'\to\gamma\gamma$. In the book of \'E. Cartan published in 1966, Dirac spinors…
We study the problem of axial and gauge anomalies in a reducible theory involving vector and tensor gauge fields coupled in a topological way. We consider that vector and axial fermionic currents couple with the tensor field in the same…
We construct the three point function involving an axial vector current and two energy-momentum tensors for four dimensional conformal field theories. Conformal symmetry determines the form of this three point function uniquely up to a…
The axial magnetic field, which couples to left- and right-handed fermions with opposite signs, may generate an equilibrium dissipationless energy flow of fermions in the direction of the field even in the presence of interactions. We…
The axial magnetic effect, i.e., the generation of an energy current parallel to an axial magnetic field coupling with opposite signs to left- and right-handed fermions is a non-dissipative transport phenomenon intimately related to the…
We derive the expression of the abelian axial anomaly in the so-called multi-Weyl and triple-point crossing semimetals. No simplifying restrictions are assumed on the symmetry of the spectrum. Three different computation methods are…
We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral…
These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…
The gapless fermionic excitations in superfluid 3He-A have a "relativistic" spectrum close to the gap nodes. They are the counterpart of the chiral particles (left-handed and right-handed) in high energy physics above the electroweak…
We investigate on the plane the axial anomaly for euclidean Dirac fermions in the presence of a background Aharonov--Bohm gauge potential. The non perturbative analysis depends on the self--adjoint extensions of the Dirac operator and the…
We consider a Dirac fermion in a metric-axial-tensor (MAT) background. By regulating it with Pauli-Villars fields we analyze and compute its full anomaly structure. Appropriate limits of the MAT background allows to recover the anomalies of…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
Weyl semimetals are predicted to realize the three-dimensional axial anomaly first discussed in particle physics. The anomaly leads to unusual transport phenomena such as the chiral magnetic effect in which an applied magnetic field induces…
We consider theories with gauged chiral fermions in which there are abelian anomalies, and no nonabelian anomalies (but there may be nonabelian gauge fields present). We construct an associated theory that is gauge-invariant,…
The axial anomaly is computed for Euclidean Dirac fermions on the plane. The dependence upon the self-adjoint extensions of the Dirac operator is investigated and its relevance concerning the second virial coefficient of the anyon gas is…