Search results for "renormalization"
showing 10 items of 470 documents
Electric-magnetic duality and renormalization in curved spacetimes
2014
We point out that the duality symmetry of free electromagnetism does not hold in the quantum theory if an arbitrary classical gravitational background is present. The symmetry breaks in the process of renormalization, as also happens with conformal invariance. We show that a similar duality-anomaly appears for a massless scalar field in $1+1$ dimensions.
Proper Time Flow Equation for Gravity
2004
We analyze a proper time renormalization group equation for Quantum Einstein Gravity in the Einstein-Hilbert truncation and compare its predictions to those of the conceptually different exact renormalization group equation of the effective average action. We employ a smooth infrared regulator of a special type which is known to give rise to extremely precise critical exponents in scalar theories. We find perfect consistency between the proper time and the average action renormalization group equations. In particular the proper time equation, too, predicts the existence of a non-Gaussian fixed point as it is necessary for the conjectured nonperturbative renormalizability of Quantum Einstein…
A comment on the relationship between differential and dimensional renormalization
1992
We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves the same finite results as dimensional renormalization without the need to modify the space time dimension.
Renormalization group improved gravitational actions: A Brans-Dicke approach
2003
A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric sat…
Fluid membranes and2dquantum gravity
2011
We study the RG flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms we derive a system of beta functions for the running surface tension, bending rigidity and Gaussian rigidity. We look for non-trivial fixed points but we find no evidence for a crumpling transition at $T\neq0$. Finally, we propose to identify the $D\rightarrow 0$ limit of the theory with two dimensional quantum gravity. In this limit we derive new beta functions for both cosmological and Newton's constants.
Flow equation of quantum Einstein gravity in a higher-derivative truncation
2002
Motivated by recent evidence indicating that Quantum Einstein Gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term $(R^2)$. The beta-functions describing the renormalization group flow of the cosmological constant, Newton's constant, and the $R^2$-coupling are computed explicitly. The fixed point (FP) properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian FP predicted by the latter is found to generalize to …
Fixed points of nonlinear sigma models in d>2
2009
Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For $d>2$ and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned.
Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex
1992
The conformal symmetry of the QCD Lagrangian for massless quarks is broken both by renormalization effects and the gauge fixing procedure. Renormalized primitive divergent amplitudes have the property that their form away from the overall coincident point singularity is fully determined by the bare Lagrangian, and scale dependence is restricted to $\delta$-functions at the singularity. If gauge fixing could be ignored, one would expect these amplitudes to be conformal invariant for non-coincident points. We find that the one-loop three-gluon vertex function $\Gamma_{\mu\nu\rho}(x,y,z)$ is conformal invariant in this sense, if calculated in the background field formalism using the Feynman ga…
Gluon mass scale through nonlinearities and vertex interplay
2019
We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the "kinetic term" of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial {\it Ans\"atze}, which are subsequently improved by means of …
Unquenching the gluon propagator with Schwinger-Dyson equations
2012
In this article we use the Schwinger-Dyson equations to compute the nonperturbative modifications caused to the infrared finite gluon propagator (in the Landau gauge) by the inclusion of a small number of quark families. Our basic operating assumption is that the main bulk of the effect stems from the "one-loop dressed" quark loop contributing to the full gluon self-energy. This quark loop is then calculated, using as basic ingredients the full quark propagator and quark-gluon vertex; for the quark propagator we use the solution obtained from the quark gap equation, while for the vertex we employ suitable Ans\"atze, which guarantee the transversality of the answer. The resulting effect is i…