Stochastic quantisation of a gauge field in the spatial axial gauge

The stochastic quantisation method of Nelson can be applied to quantise an Abelian gauge field in the spatial axial gauge.     

On the realization of Landau gauge

Starting with the determination of the two-points function in the Landau gauge given by Wightman and Strocchi, we build a more economic realization of this gauge, following the basic principles they have proposed.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.     

A note on gauge symmetry breaking

We show that the breaking of Abelian gauge symmetry implies the existence of dipole singularities in the correlation functions of the (Abelian) Higgs model. We also show that the noninvariance of the Wightman functions does not preclude the implementability of the global gauge symmetry. An explicit example of gauge symmetry breaking (Ferrari's model) is discussed.     

A note on global gauge anomalies

Using methods of group cohomology the definitions of global and local anomalies are revisited taking into account the fact that the action of the gauge group on the space of connections is not free. The global SU (2) anomaly appears as an abelian one.     

Chiral symmetry breaking beyond the Landau gauge

By using novel Ansätze for the longitudinal and transverse parts of the fermion-gauge boson vertex that respect the Ward identify and multiplicative renormalizability, we demonstrate that chiral symmetry breaking occurs in vector-like gauge theories in such a way that the critical coupling constant and dynamical mass function are gauge-independent, at least in leading order.     

Coherent Landau states with gauge invariance

Coherent states for the Landau system (planar charged particle moving in a uniform magnetic field) are developed. It is convenient to use these states to describe the circular motion of the charged particle. The results obtained do not depend on gauges.     

Stochastic quantisation of a gauge field in the infrared-soft flow gauges

Quantisation of the Abelian gauge field in some classes of the noncovariant infrared-soft gauges can be carried out consistently based on the classical field equations and the basic principles of stochastic mechanics.     

Elliptic operators in the functional quantisation for gauge field theories

Given a gauge theory with gauge groupG acting on a path spaceX,G andX being both infinite dimensional manifolds modelled on spaces of sections of vector bundles on a compact riemannian manifold without boundary, it is shown that when the action ofG onX is smooth, free and proper, the same ellipticity condition on an operator naturally given by the geometry of the problem yields both the existence of a principal fibre bundle structure induced by the canonical projection :XX/G and the existence of the Faddeev-Popov determinant arising in the functional quantisation of the gauge theory. This holds for certain gauge theories with anomalies like bosonic closed string theory in non-critical dimension and also holds for a class of gauge theories which includes Yang-Mills theory.     

Landau parameters and pairing-on the shores of the nuclear Fermi sea

We present a systematic scheme for calculating the ground-state energy, single-particle energies and the effective mass, Fermi-liquid parameters, and pairing matrix elements for nuclear and neutron matter with realistic state-dependent interactions. The method retains much of the clarity of more conventional treatments while permitting reliable numerical calculations. Deficiencies in the central Jastrow correlation operator ansatz are largely overcome by low-order perturbation theory in the correlated basis generated by the Jastrow operator. Calculations of these quantities are presented for the Reid and Bethe-Johnson interactions. An analysis of the results emphasizes the importance of state-dependent correlations arising directly from the interaction or indirectly through many-body effects. The numerical results provide insight into the actual structure of the self-energy operator in nuclear and neutron matter and into the usefulness of sum rules for the quasiparticle interaction and the Landau parameters.     

Fano Resonance in Landau Fermi and Luttinger Liquids

With a two-channel model, we study the influence of temperature, external voltage and magnetic flux on the line shape of the Fano resonance, and show that in the Luttinger liquid case, the background transmittance and the asymmetric parameter depend strongly on the temperature and external voltage, while for the Landau Fermi liquid case they are nearly independent of these parameters in the low energy region. Moreover, we demonstrate that the asymmetric parameter changes periodically with an external magnetic flux, which is consistent with the recent experimental data.     

Ghost condensates in Yang-Mills theories in the Landau gauge

Ghost condensates of dimension 2 are analyzed in pure SU(N) Yang-Mills theories by combining the local composite operators technique with the algebraic BRST renormalization.     

Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

We study the strong-coupling limit β=0 of lattice SU(2) Landau gauge Yang–Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite β. In turn, the gluon propagator only mildly depends on the Gribov ambiguity.     

The Landau gauge gluon propagator in lattice QCD

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4³ × 8 lattices), β = 5.8 (400 4³ × 10 lattices and 100 6³ × 12 lattices), and β = 6.0 (100 4³ × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.     

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit β=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^{2}\ll\varLambda_{\mathrm{QCD}}^{2}$ . In the strong-coupling limit, this same behavior is obtained for the larger values of a ² q ² (in units of the lattice spacing a), where it is otherwise swamped by the gauge-field dynamics. Deviations for a ² q ²<1 are well parameterized by a transverse gluon mass ∝1/a. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes (Phys. Rev. D 81:016005, 2010).