Classical transport theory is employed to analyze the hot quark-gluon plasma at the leading order in the coupling constant. A condition on the (covariantly conserved) color current is obtained.From this condition, the generating functional of hard thermal loops with an arbitrary number of soft external bosonic legs can be derived. Our approach, besides being more direct than alternative ones, shows that hard thermal loops are essentially classical.

Classical transport theory for colored particles is investigated and employed to derive the hard thermal loops of QCD. A formal construction of phasespace for color degrees of freedom is presented. The gauge invariance of the non-Abelian Vlasov equations is veried and used as a guiding principle in our approximation scheme. We then derive the generating functional of hard thermal loops from a constraint satised at leading-order by the color current.This derivation is more direct than alternative ones based on perturbative quantum eld theory, and shows that hard thermal eects in hot QCD are essentially classical.As an illustration, we analyze color polarization in the QCD plasma.

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A graph is matching covered if it connected, has at least two vertices and each of its edges is contained in a perfect matching. A 3-connected graph G is a brick if, for any two vertices u and v of G, the graph G − {u, v} has a perfect matching. As shown by Lovász [Matching structure and the matching lattice, J. Combin. Theory Ser. B 43 (1987) 187-222] every matching covered graph G may be decomposed, in an essentially unique manner, into bricks and bipartite graphs known as braces. The number of bricks resulting from this decomposition is denoted by b(G).The object of this paper is to present a recursive procedure for generating bricks. We define four simple operations that can be used to construct new bricks from given bricks. We show that all bricks may be generated from three basic bricks K 4 , C 6 and the Petersen graph by means of these four operations. In order to establish this, it turns out to be necessary to show that every brick G distinct from the three basic bricks has a thin edge, that is, an edge e such that (i) G − e is a matching covered graph with b(G − e) = 1 and (ii) for each barrier B of G − e, the graph G − e − B has precisely |B| − 1 isolated vertices, each of which has degree two in G − e. Improving upon a theorem proved in [M.H. de Carvalho, C.L. Lucchesi, U.S.R. Murty, On a conjecture of Lovász concerning bricks, I, The characteristic of a matching covered graph, J. Combin. Theory Ser. B 85 (2002) 94-136; M.H. de Carvalho, C.L. Lucchesi, U.S.R. Murty, On a conjecture of Lovász concerning bricks, II, Bricks of finite characteristic, J. Combin. Theory Ser. B 85 (2002) 137-180] we show here that every brick different from the three basic bricks has an edge that is thin.A cut of a matching covered graph G is separating if each of the two graphs obtained from G by shrinking the shores of the cut to single vertices is also matching covered. A brick is solid if it does not have any nontrivial separating cuts. Solid bricks have many interesting properties, but the complexity status of deciding whether a given brick is solid is not known. Here, by using our theorem on the existence of thin edges, we show that every simple planar solid brick is an odd wheel.

We show that the BF theory in any space-time dimension, when quantized in a certain linear covariant gauge, possesses a vector supersymmetry. The generator of the latter together with those of the BRS transformations and of the translations form the basis of a superalgebra of the Wess-Zumino type. We give a general classification of all possible anomalies and invariant counterterms. Their absence, which amounts to ultraviolet finiteness, follows from purely algebraic arguments in the lower-dimensional cases.