Search results for "Mathematical physics"
showing 10 items of 2687 documents
Nonperturbative study of the four gluon vertex
2014
In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale $p$ is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The orig…
Infrared singularities of QCD amplitudes with massive partons
2009
A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevant for massless partons does not carry over to the case with massive legs, where starting at two-loop order new color and momentum structures arise, which are not of the color-dipole form. The resulting two-loop three-parton correlations can be expressed in terms of two functions, for which some genera…
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…
Quantum geometry and microscopic black hole entropy
2006
9 pages, 6 figures.-- PACS nrs.: 04.60.Pp, 04.70.Dy.-- ISI Article Identifier: 000242448900013.-- Published online on Nov 28, 2006.
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 …
Integrands of loop amplitudes within loop-tree duality
2020
Using loop-tree duality, we relate a renormalised $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularised $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show that up to three loops the latter object is easily computable from recurrence relations. This defines an integrand of the loop amplitude with a global definition of the loop momenta. Field and mass renormalisation are performed in the on-shell scheme.
Gravity, Non-Commutative Geometry and the Wodzicki Residue
1993
We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat kernel expansion of $D^{2}$. We use this result to derive a gravity action for commutative geometry which is the usual Einstein Hilbert action and we also apply our results to a non-commutative extension which, is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological co…
Functions Characterizing the Ground State of the XXZ Spin-1/2 Chain in the Thermodynamic Limit
2013
We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-1/2 chain in the disordered regime. In particular, we obtain lower and upper bounds for the dressed energy, dressed charge and density of Bethe roots. Furthermore, we establish that given a fixed external magnetic field (or a fixed magnetization) there exists a unique value of the boundary of the Fermi zone.
The kite integral to all orders in terms of elliptic polylogarithms
2016
We show that the Laurent series of the two-loop kite integral in $D=4-2\varepsilon$ space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using differential equations we present an iterative method to compute any desired order. As an example, we give the first three orders explicitly.
Feynman integrals and iterated integrals of modular forms
2017
In this paper we show that certain Feynman integrals can be expressed as linear combinations of iterated integrals of modular forms to all orders in the dimensional regularisation parameter $\varepsilon$ . We discuss explicitly the equal mass sunrise integral and the kite integral. For both cases we give the alphabet of letters occurring in the iterated integrals. For the sunrise integral we present a compact formula, expressing this integral to all orders in $\varepsilon$ as iterated integrals of modular forms.