Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStudy of a gauge invariant local composite fermionic field
112
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this work, we study a gauge invariant local non-polynomial composite spinor field in the fundamental representation in order to establish its renormalizability. Similar studies were already done in the case of pure Yang-Mills theories where a local composite gauge invariant vector field was obtained and an invariant renormalizable mass term could be introduced. Our model consists of a massive Euclidean Yang-Mills action with gauge group $SU(N)$ coupled to fermionic matter in the presence of an invariant spinor composite field and quantized in the linear covariant gauges. The whole set of Ward identities is analysed and the algebraic proof of the renormalizability of the model is obtained to all orders in a loop expansion.
rate research
Read More
The spectral properties of a set of local gauge (BRST) invariant composite operators are investigated in the $SU(2)$ Yang--Mills--Higgs model with a single Higgs field in the fundamental representation, quantized in the t Hooft $R_{xi}$-gauge. These operators can be thought of as a BRST invariant version of the elementary fields of the theory, the Higgs and gauge fields, with which they share a gauge independent pole mass. The two-point correlation functions of both BRST invariant composite operators and elementary fields, as well as their spectral functions, are investigated at one-loop order. It is shown that the spectral functions of the elementary fields suffer from a strong unphysical dependence from the gauge parameter $xi$, and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.
The renormalization properties of two local BRST invariant composite operators, $(O,V_mu)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the $U(1)$ Higgs model by means of the algebraic renormalization setup. Their renormalization $Z$s factors are explicitly evaluated at one-loop order in the $overline{text{MS}}$ scheme by taking into due account the mixing with other gauge invariant operators. In particular, it turns out that the operator $V_mu$ mixes with the gauge invariant quantity $partial_ u F_{mu u}$, which has the same quantum numbers, giving rise to a $2 times 2$ mixing matrix. Moreover, two additional powerful Ward identities exist which enable us to determine the whole set of $Z$s factors entering the $2 times 2$ mixing matrix as well as the $Z$ factor of the operator $O$ in a purely algebraic way. An explicit check of these Ward identities is provided. The final setup obtained allows for computing perturbatively the full renormalized result for any $n$-point correlation function of the scalar and vector composite operators.
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 construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.
Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of non-polynomial and cubic string field theories are discussed. To have a possibility to deal with both GSO(+) and GSO(-) sectors in the uniform way a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open string field theories truncated pure gauge configurations parameterized by wedge states play an essential role. The matrix form of this parametrization for the NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equation of motion on the subspace of the wedge states. The perturbation expansion is cured by adding extra terms that are nothing but the terms necessary for the equation of motion contracted with the solution itself to be satisfied.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
