THEORY OF FIELDS

Author: SEIJAS NAYA CISAR.
Year: 2006.
University: SANTIAGO DE COMPOSTELA [www.usc.es].
Place of defense: FACULTAD DE CIENCIAS FMSICAS.
Place of preparation: FACULTAD DE CIENCIAS FMSICAS, UNIVERSIDAD DE SANTIAGO DE COMPOSTELA.

Summary: Renormalizacisn differential is a mitodo of renormalizacisn in the space of positions that was to replace words that are too divergent to have a well-defined Fourier transform, derived from other expressions less unique. In this procedure has been introduced with dimensions of a constant mass M to parameterize the ambig | Local age. Due to a change in M can be reabsorbed in a reescalamiento of the coupling constant, this suggests that the amplitudes renormalizadas satisfy equations group renormalizacisn, playing the role of M-scale group renormalizacisn. This paper has studied the renormalizacisn expression differences that have UV and IR. In renormalizar a teorma having both types of differences, it must be borne in mind that both renormalizaciones have to be decoupled, thus implying that the two scales (IR and UV) must be independent. One of the caractermsticas most important renormalizacisn differential is that the gauge invariance is preserved. However, due to the ambiguities that are produced in the mitodo of renormalizacisn, be imposed on each calculation (with a teorma gauge) Ward identities so explmcita, so that in fixing scheme renormalizacisn. The fact that preserves gauge invariance is reflected in the fact that it is always possible to satisfy these identities with expressions renormalizadas (except of course the anomalmas). To avoid the need to impose the identities of Ward explmcitamente in each calculation, it desarrolls Renormalizacisn Differential Restricted (RDR). This mitodo is to provide a set of rules that set a priori ambiguity inherent in the whole process, so that expressions renormalizadas are directly gauge invariant (it is not necessary to impose the identities of Ward). Applying these rules, we get a set of basic expressions renormalizadas. Therefore, the process of renormalizacisn consists of two parts: the first phase will perform all contractions mndices (RDR not switch to this operacisn) and writes expresisn naked in tirminos of these basic functions. In a second step, these functions are replaced by their values renormalizados. Although RDR has developed sslo to calculate a loop provides informacisn ztil when trying calculations to two loops. This paper shows that apply RDR fixed unmvocamente coefficients of all logarithms of the scales in expresisn two loops renormalizada, which are tirminos we need to assess the ecuacisn group renormalizacisn. That is why, to obtain expressions renormalizadas two loops, it will take into account the possible tirminos premises that are generated. Distinguiremos two different situations: differences with nested diagrams and charts with overlap. - Divergences nested: In this case, it starts imposing RDR to subdivergencia. By doing so, we set the tirminos local loop we have in the diagram, along with the logarithms of the scales for a loop. So, in considering the expresisn complete diagram and implement renormalizacisn differential normal, we are all factors that relate to logarithms of the scales are unmvocamente certain, as the tirminos local loop (to be promoted to logarithms) have been set by RDR. - Divergences with overlapping: In the case of discrepancies with overlapping, situacisn is more complicated, since it is often difmcil recognize expressions to a loop to which must be applied starting RDR. Therefore, what we have done is to obtain a complete set of integrated renormalizadas with overlap, as much from four acting on the propagators and two mndices free. With this list we can get the expresisn two points renormalizada any teorma with acoplos derivative, which means that, by applying the mitodo camp background, we can get funcisn beta. To evaluate integrals are used basically two mitodos: 1 .- By igua 8 ldades i 688 ntegrales is rescriben integrals in tirminos other having a d'almbertiano acting on one of the propagators. 2 .- Use the descomposicisn partly trace and without trace imposed RDR to funcisn basic three propagators. This procedure has reobtenido the funcisn beta two loops of QED and extensisn supersimitrica, SuperQED, habman been obtained previously in the context of renormalizacisn differential applying Ward identities. Tambiin have obtained the beta features two loops of teormas of Yang-Mills and Super Yang-Mills. In the case of Super Yang-Mills, mitodo we use presents a clear advantage over mitodos dimensional usual, as it allows to differentiate between the IR and UV divergences affecting this teorma because of the way the gauge propagator. Similarly, one can conclude that the origin of the ratio of two loops of funcisn beta comes from the UV scale of the subdivergencia, two loops survives thanks to the existence of IR divergences.