A non-commutative walecka model as an effective theory for interacting nucleons of finite size

Groenewald, Hendrikus Wilhelm. (2012-03)

Thesis (MSc)--Stellenbosch University, 2012.

Thesis

ENGLISH ABSTRACT: The nite size of nucleons should play an important role in the description of high density nuclear matter as found in astro-physical objects. Yet we see that the Walecka model, which is generally used to describe these systems, treats the nucleons as point particles. Here we argue that a non-commutative version of the Walecka model may be a consistent and appropriate framework to describe nite nucleon size e ects. In this framework the length scale introduced through the non-commutative parameter plays the role of the nite nucleon size. To investigate the consequences of this description, the equations of motion and energy-momentum tensor for the non-commutative Walecka model are derived. We also derived an expression for the total energy of the system, as a function of the non-commutative parameter, in a spatially non-uniform matter approximation. The non-commutative parameter, as a variable dependent on the dynamics of the system, remains to be solved self-consistently.

AFRIKAANSE OPSOMMING: Die eindige grootte van nukleone moet 'n belangrike rol speel in die beskrywing van ho e-digtheid kern materie soos gevind in astro- siese voorwerpe. Tog sien ons dat die Walecka model, wat in die algemeen gebruik word om hierdie stelsels te beskryf, die nukleone as punt deeltjies hanteer. Ons redeneer dus dat 'n nie-kommutatiewe weergawe van die Walecka model 'n konsistente en gepaste raamwerk is om die e ekte van eindige nukleon grootte te beskryf. In hierdie raamwerk speel die lengte-skaal wat ingevoer word deur die nie-kommutatiewe parameter die rol van eindige grootte vir nukleone. Om die gevolge van hierdie beskrywing te ondersoek, word die vergelykings van beweging en die energie-momentum tensor afgelei vir die nie-kommutatiewe Walecka model. Ons het ook 'n uitdrukking vir die totale energie van die stelsel, as 'n funksie van die niekommutatiewe parameter, afgelei in 'n ruimtelik nie-uniforme materie benadering. Die niekommutatiewe parameter, as 'n veranderlike afhanklik van die dinamika van die stelsel, bly steeds om self-konsistent opgelos te word.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/20255
This item appears in the following collections: