We prove that β-function of the gauge coupling in 2 + 1D gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.

In this letter we discuss the Higgs mechanism in the linear and static translational gauge theory of dislocations. We investigate the role of the Nambu-Goldstone field and the Proca field in the dislocation gauge theory. In addition, we give the constitutive relations for (homogeneous) anisotropic, hemitropic and isotropic materials and also stress function tensors for the gauge theory of dislo...

The manifestly gauge invariant exact renormalisation group provides a framework for performing continuum computations in SU (N) Yang-Mills theory, without fixing the gauge. We use this formalism to compute the two-loop β function in a manifestly gauge invariant way, and without specifying the details of the regularisation scheme.

The connnement criterion based on the dependence of the partition function on the boundary condition for the electric eld strength is presented for the non{abelian gauge theory. It is supported by an approximate calculation of the partition function and the Wilson loop for SU(N) gluodynamics in the 3-d Fock{Schwinger gauge. Possible directions of further studies of connnement are outlined.

Among various approaches in proving gauge independence, models containing an explicit gauge dependence are convenient. The well-known example is the gauge parameter in the covariant gauge fixing which is of course most suitable for the perturbation theory but a negative metric prevents us from imaging a dynamical picture. Noncovariant gauge such as the Coulomb gauge is on the contrary used for ...

It is proposed to use the pinch technique to obtain the gauge-independent thermal β function βT in a hot Yang-Mills gas. Calculations of βT are performed at one-loop level in four different gauges, (i) the background field method with an arbitrary gauge parameter, (ii) the Feynman gauge, (iii) the Coulomb gauge, and (iv) the temporal axial gauge. When the pinch contributions to the gluon self-e...

In the earlier works on quantum geometrodynamics in extended phase space it has been argued that a wave function of the Universe should satisfy a Schrödinger equation. Its form, as well as a measure in Schrödinger scalar product, depends on a gauge condition (a chosen reference frame). It is known that the geometry of an appropriate Hilbert space is determined by introducing the scalar product,...

This paper applies a fully post-Newtonian theory (Damour et al. 1991, 1992, 1993, 1994) to the problem of gauge in relativistic reference systems. Gauge fixing is necessary when the precision of time measurement and application reaches 10−16 or better. We give a general procedure for fixing the gauges of gravitational potentials in both the global and local coordinate systems, and for determini...

To solve the low-frequency breakdown inherent from the electric field integral equation (EFIE), an alternative new form of the EFIE is proposed by using the Coulomb-gauge Green’s function of quasi-static approximation. Different from the commonly adopted Lorentz-gauge EFIE, the Coulomb-gauge EFIE separates the solenoidal and irrotational surface currents explicitly, which captures inductive and...

We study the graviton self-energy function in a general gauge, using a hard thermal loop expansion which includes terms proportional to T 4, T 2 and log(T ). We verify explicitly the gauge independence of the leading T 4 term and obtain a compact expression for the sub-leading T 2 contribution. It is shown that the logarithmic term has the same structure as the ultraviolet pole part of the T = ...