Using Covariant Polarisation Sums in QCD

Covariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, $$\sum _{\lambda } \varepsilon _\mu ^{(\lambda )}\varepsilon _\nu ^{(\lambda )*} = -\eta _{\mu \nu }$$ ∑ λ ε μ ( λ ) ε ν ( λ ) ∗ = - η μ ν , is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev–Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms $$\mathcal {A}(c_1,\bar{c}_1;\ldots )\mathcal {A}(\bar{c}_1,c_1;\ldots )^*$$ A ( c 1 , c ¯ 1 ; … ) A ( c ¯ 1 , c 1 ; … ) ∗ between ghost amplitudes cannot be transformed into $$(-1)^{n/2}|\mathcal {A}(c_1,\bar{c}_1;\ldots )|^2$$ ( - 1 ) n / 2 | A ( c 1 , c ¯ 1 ; … ) | 2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.

On the internal geometry of the trajectories of charged particles in symmetric external fields

The curvature and torsion of the trajectories of charges in external gauge fields, including the fields of magnetic monopoles, are calculated. It is shown that these quantities are efficiently calculated using the equations of motion and first integrals. For a wide class of magnetic fields, their form-invariant combination was found.

Anomalous transport phenomena and momentum space topology

Using the derivative expansion applied to the Wigner transform of the two - point Green function this is possible to derive the response of various nondissipative currents to the external gauge fields. The corresponding currents are proportional to the momentum space topological invariants. This allows to analyse systematically various anomalous transport phenomena including the anomalous quantum Hall effect and the chiral separation effect. We discuss the application of this methodology both to the solid state physics and to the high energy physics.

Current–current correlation function in 3D massive Dirac theory with chemical potential

The response of fermionic system to external gauge fields is defined by current–current correlation function Πμν(q, q0). Transport properties of different physical quantities are determined by zero energy–momentum limit of it. As it is known close to half-filling the physics of graphene is described by (2+1)-dimensional Dirac theory. In this paper, we calculate current–current correlation function in Dirac theory in a presence of chemical potential η and gap m.

PARITY ANOMALY IN DIRAC EQUATION IN (1+2) DIMENSIONS, QUANTUM ELECTRODYNAMICS AND PAIR PRODUCTION

We show that parity operator plays an interesting role in Dirac equation in (1+2) dimensions and can be used for defining chiral charges. Further the "anomalous" current induced by an external gauge field can be related to the anomalous divergence of an axial vector current which arises due to quantum radiative corrections provided by triangular loop Feynman diagrams in analogy with the corresponding axial anomaly in (1+3) dimensions. It is shown that the nonconservation of "chiral charge" due to anomaly is related with the topological Chern–Simons charge. As an application pair creation of massless fermions in electric field is discussed.