Summation and Renormalization of Bubble Graphs to All Orders
نویسنده
چکیده
We introduce the 2PPI expansion which sums the bubble graphs to all orders. We show that this expansion can be renormalised with the usual counterterms in a mass independent scheme. We discuss its application to the O(N) linear σ-model.
منابع مشابه
The 2ppi Expansion: Dynamical Mass Generation and Vacuum Energy *
LTH–601 We discuss the 2P P I expansion, a summation of the bubble graphs up to all orders, by means of the 2D Gross-Neveu toy model, whose exact mass gap and vacuum energy are known. Then we use the expansion to give analytical evidence that a dimension two gluon condensate exists for pure Yang-Mills in the Landau gauge. This A a µ A a µ condensate consequently gives rise to a dynamical gluon ...
متن کاملClosed-Form Summation of RG-Accessible Logarithmic Contributions to Semileptonic B-Decays and Other Perturbative Processes
For any perturbative series that is known to k-subleading orders of perturbation theory, we utilise the process-appropriate renormalization-group (RG) equation in order to obtain all-orders summation of series terms proportional to α log ( μ ) with k = {0, 1, 2, 3}, corresponding to the summation to all orders of the leading and subsequent-three-subleading logarithmic contributions to the full ...
متن کاملQuantum Field Theory in the Limit x ≪ 1 1
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x ≪ 1. Particular emphasis is paid to theories with interactions involving more than one field where it is found that a matrix renormalization is necessary. Asymptotic scaling forms, in agreement with Regge theory, are derived fo...
متن کاملDetermining the Likelihood of Damage in Concrete and its Physical Structure
Applying renormalization group theory to evaluate the safety of overall structure, local damage probability must be obtained at first. According to the results of unit detection test and numerical simulation, the methods how to determine local damage probability was presented in the paper. For small unit, meaning the unit size is far less than the maximum primitive cell or the structure size, i...
متن کاملRenormalization of noncommutative φ-theory by multi-scale analysis
In this paper we give a much more efficient proof that the real Euclidean φ4model on the four-dimensional Moyal plane is renormalizable to all orders. We prove rigorous bounds on the propagator which complete the previous renormalization proof based on renormalization group equations for non-local matrix models. On the other hand, our bounds permit a powerful multi-scale analysis of the resulti...
متن کامل