String Variables in Quantum Chromodynamics

Abstract

There has been recently an increasing interest to formulate gauge field theories in terms of the gauge invariant string variables (“path dependent phase factors”). There are several reasons for this. One of them is the close similarity of the classical gauge field dynamics (if formulated in terms of string variables) with the quantum mechanics of relativistic strings [l,2]. In this connection a number of authors [3–6] derived the dynamical equations for string variables in classical gauge field theories. Others [7–8] showed that the gauge fields can be considered as the lowest excitations of a condensate of relativistic strings. Another motivation for introducing string variables is that they are gauge invariant and therefore explicitly solve the otherwise rather complicated constraints resulting from gauge invariance [9–12]. A third important aspect of using string variables is that confinement [12] and duality [13–14] properties of the quantum gauge fields may be simply expressed in terms of them.