Overlap in odd dimensions

In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes, only at the expense of parity invariance. When parity invariance is enforced invariance under small gauge transformations can be maintained and continuum global gauge anomalies are reproduced.     

Collective excitations of massive Dirac particles in a hot and dense medium

The one-loop dispersion relation which defines the collective excitations of massive Dirac particles in a hot and dense quark-gluon medium is obtained in the high-temperature limit for the case m≪gT and is solved explicitly for all |q| when μ=0. Four well-separated spectrum branches (quasi-particle and quasi-hole excitations) are found, and their behaviors for small and large |q| are investigated. All calculations are performed using the temperature Green function technique and fixing the Feynman gauge. The gauge dependence of the spectra found is briefly discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 3–8 (10 January 1998) Published in English in the original Russian journal. Edited by the Steve Torstveit.     

Anomalies and odd dimensions

The parity-violating effective action for theories of fermions coupled to external gauge and gravitational fields in odd dimensions is computed exactly. This action is then used to compute gauge and gravitational anomalies in even dimensions. This derivation of the anomalies elucidates the relation of covariant to consistent anomalies as well as the relation between the Abelian anomaly and the non-Abelian anomaly in two lower dimensions.     

Dirac semimetal in three dimensions

We show that the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials. Unlike in phase transitions from inversion symmetric topological to normal insulators, we show that particular space groups also allow 3D Dirac points as symmetry protected degeneracies. We provide criteria necessary to identify these groups and, as an example, present ab initio calculations of β-cristobalite BiO(2) which exhibits three Dirac points at the Fermi level. We find that β-cristobalite BiO(2) is metastable, so it can be physically realized as a 3D analog to graphene.     

Dirac field in topologically massive gravity

We consider a Dirac field coupled minimally to the Mielke–Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological constant.     

Chiral anomalies in even and odd dimensions

Odd dimensional Yang-Mills theories with an extra topological mass term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.     

Different varieties of massive Dirac neutrinos

The concept of Majorana and Dirac massive neutrinos is discussed for the case in which there are several types, or flavors, of leptons. Different varieties of Dirac neutrinos are possible, distinguised by their magnetic moments and anomalous interactions with probabilities proportional to (m/E)².     

Nonperturbative inconsistency of stochastic quantization in odd dimensions

It is shown that a stochastically-quantized theory of interacting fermion and gauge fields in odd spacetime dimensions can be renormalized, preserving both gauge- and parity-invariance. Thus, the pertinent parity-violating anomalies are not reproduced by the stochastic quantization. Moreover, this theory does not possess a nonperturbative equilibrium limit unless one introduces an appropriate parity-violating counterterm. We conclude that an odd-dimensional gauge theory with fermions cannot be inconsistently quantized in the stochastic scheme unless the parity-violating anomales cancel.     

Nonperturbative inconsistency of stochastic quantization in odd dimensions

It is shown that a stochastically-quantized theory of interacting fermion and gauge fields in odd spacetime dimensions can be renormalized, preserving both gauge-and parity-invariance. Thus, the pertinent parity-violating anomalies are not reproduced by the stochastic quantization. Moreover, this theory does not possess a nonperturbative equilibrium limit unless one introduces an appropriate parity-violating counterterm. We conclude that an odd-dimensional gauge theory with fermions cannot be consistently quantized in the stochastic scheme unless the parity-violating anomalies cancel.     

Shubnikov-de Haas oscillations of massive Dirac fermions in a Dirac antiferromagnet SrMnSb2

We investigate the physical properties of massive Dirac fermions in SrMnSb₂ using transport, specific heat, electronic structure calculations, and Shubnikov-de Haas (SdH) oscillations. SrMnSb₂ is a candidate Dirac antiferromagnet, consisting of the MnSb layers and the distorted square net of Sb atoms with a zigzag chain structure. This structural distortion leads to gap opening at the band crossing point found in the square lattice of the sister compound SrMnBi₂ but leaves another Dirac band crossing near the Brillouin zone boundary. The small 2D Fermi surface with a light electron mass and a small Fermi energy is confirmed by the large resistivity anisotropy, the large Seebeck coefficient, and also the angle and temperature dependent SdH oscillations. The Berry phase obtained from the SdH oscillations is trivial, in contrast to the case of SrMnBi₂. The relatively large spin orbit coupling gap and the small Fermi energy in SrMnSb₂ is found to be essential to understand this contrasting behavior of the massive Dirac fermions as compared to SrMnBi₂. Our observations demonstrate that the Berry phase of the mobile electrons in SrMnSb₂ is sensitive to the Fermi level change and can be tuned by doping or deficiency.     

Interaction of goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields

Interaction of Goldstone particles in two dimensions lead to the infrared catastrophe. In order to analyze it we apply to the problem the method of the renormalization group. It is shown that due to interaction the regime of the “asymptotic freedom” arises. The continuation to higher dimensions and the applications of the result are briefly discussed.     

Consistent massive anomalous dimensions

We re-evaluate the O(g²) momentum-subtracted anomalous dimensions of QCD with massive quarks. The QCD equations of motion are used to relate operator matrix elements with different tensor structures. This procedure yields explicitly gauge-invariant anomalous dimensions. Our results differ slightly from those in the literature. The forward Compton amplitude for scattering of massive quarks and a scalar current is examined. The large Q² behavior of this amplitude is shown to be simply related to the momentum-subtracted, mass-dependent anomalous dimension.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Supersymmetric Dirac particles in Riemann-Cartan space-time

A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of and thus complete the partial results of previous WKB calculations. We touch also on such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass.     

On the massive Dirac neutrino radiative decay

The presence of right-handed currents and left-right mixing contributes to the neutrino radiative decay amplitude a term that is directly proportional to the charged lepton mass. This has led to the suggestion that observable decays of relic neutrinos might occur in the left-right model or the mirror model. Explicit calculations in these models are carried out including a careful analysis of the origin of neutrino mass, here assumed to be a Dirac mass. It is found that the amplitude is proportional to the neutrino mass and thus too small to be of interest. A brief comment on the neutrino magnetic moment in anSU(2) _L ×U(1) _Y model, which contains an iso-singlet charged scalar η⁺, is also presented.