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Register a new userOn a renormalizable class of gauge fixings for the gauge invariant operator $A_{min }^{2}$
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The dimension two gauge invariant non-local operator $A_{min }^{2}$, obtained through the minimization of $int d^4x A^2$ along the gauge orbit, allows to introduce a non-local gauge invariant configuration $A^h_mu$ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both $A_{min }^{2}$ and $A^{h}_mu$ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of $A_{min }^{2}$ gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as t Hoofts $R_zeta$-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.
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We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A^2_{rm min}$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A^2_{rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A^2_{rm min}$ turns out to be independent from the gauge parameter $alpha$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.
We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.
We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon is produced.
We study the Gluino-Glue operator in the context of Supersymmetric ${cal N}{=}1$ Yang-Mills (SYM) theory. This composite operator is gauge invariant, and it is directly connected to light bound states of the theory; its renormalization is very important as a necessary step for the study of low-lying bound states via numerical simulations. We make use of a Gauge-Invariant Renormalization Scheme (GIRS). This requires the calculation of the Greens function of a product of two Gluino-Glue operators, situated at distinct space-time points. Within this scheme, the mixing with non-gauge invariant operators which have the same quantum numbers is inconsequential. We compute the one-loop conversion factor relating the GIRS scheme to $overline{rm MS}$. This conversion factor can be used in order to convert to $overline{rm MS}$ Greens functions which are obtained via lattice simulations and are renormalized nonperturbatively in GIRS.
We consider non-linear wave type solutions with mass scale parameter and vahished canonical spin density operator in a pure SU(2) quantum chtomodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered non-linear wave type solutions have common features: presence of a mass scale parameter, non-vanishing projection of the color magnetic field along the propagation direction and zero spin density. The last property requires revision of the gauge invariant definition of the spin density operator which supposed to be massless vector field in the classical theory. We construct a gauge invariant definition of the classical gluon spin density which is unique and Lorentz frame independent.
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