Related papers: Comments on the Gribov Ambiguity

Using the hamiltonian framework, we analyze the Gribov problem for U(N) and SU(N) gauge theories on a cylinder (= (1+1) dimensional spacetime with compact space S^1). The space of gauge orbits is found to be an orbifold. We show by explicit…

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear…

Let $M$ be an orientable, simply-connected, closed, non-spin 4-manifold and let $\mathcal{G}_k(M)$ be the gauge group of the principal $G$-bundle over $M$ with second Chern class $k\in\mathbb{Z}$. It is known that the homotopy type of…

The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional manifolds. To be more specific, we study gauge groups of…

We analyse the homotopy types of gauge groups for principal $U(n)$-bundles over lens spaces.

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure…

We study the quantization of abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the non-triviality of the…

We analyse the homotopy types of gauge groups of principal U(n)-bundles associated to pseudo Real vector bundles in the sense of Atiyah. We provide satisfactory homotopy decompositions of these gauge groups into factors in which the…

It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang-Mills theories, in particular in the low momentum regime where standard perturbation theory based on the…

We determine the number of distinct fibre homotopy types for the gauge groups of principal $Sp(2)$-bundles over a closed, simply-connected four-manifold.

We examine the relation between the gauge groups of $\mathrm{SU}(n)$- and $\mathrm{PU}(n)$-bundles over $S^{2i}$, with $2\leq i\leq n$, particularly when $n$ is a prime. As special cases, for $\mathrm{PU}(5)$-bundles over $S^4$, we show…

Connected components of $\Map(S^4,B\SU(2))$ are the classifying spaces of gauge groups of principal $\SU(2)$-bundles over $S^4$. Tsukuda [Tsu01] has investigated the homotopy types of connected components of $\Map(S^4,B\SU(2))$. But…

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in space-time dimension d<=4 is presented. The method is based on the…

Let $Y$ be a pointed space and let $\mathcal E(Y^r)$ be the group of based self-equivalences of $Y^r$, $r\geq 2$. For $Y$ a homotopy commutative $H$-group we construct a subgroup $\mathcal E_{\mathrm{Mat}}(Y^r)$ of $\mathcal E(Y^r)$ which…

We prove that the space of gauge equivalence classes of U(1)-invariant connections on some SU(2)-principle bundles over the 4-sphere S^4 is weakly homotopy equivalent to a component of the second loop space of the 2-sphere S^2.

Let $M_{l,m}$ be the total space of the $S^3$-bundle over $S^4$ classified by the element $l\sigma+m\rho\in{\pi_4(SO(4))}$, $l,m\in\mathbb Z$. In this paper we study the homotopy theory of gauge groups of principal $G$-bundles over…

We construct the homotopy pullback of $A_n$-spaces and show some universal property of it. As the first application, we review the Zabrodsky's result which states that for each prime $p$, there is a finite CW complex which admits an…

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitational gauge interactions is discussed. SU(N) gauge interactions and gravitational gauge interactions are formulated on the similar basis and…

Let P be a principal bundle with semisimple compact simply connected structure group G over a compact simply connected four-manifold M. In this note we give explicit formulas for the rational homotopy groups and cohomology algebra of the…

Complete gauge-fixing beyond perturbation theory in non-Abelian gauge theories is a non-trivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In…