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Nucleons, 2012 100к
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Описание:
by Hendrikus Wilhelm GROENEWALD Thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Physics at Stellenbosch University Supervisor : Prof. Frederik G. Scholtz Co-supervisor : Dr. Shaun M. Wyngaardt Faculty of Science Department of Physics March 2012
Автор:
xsy
Создан:
19 марта 2013 в 14:54 (текущая версия от 28 октября 2013 в 23:23)
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1 a non-commutative walecka model as an effective
theory for interacting nucleons of finite size
declaration
by submitting this thesis electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the sole author thereof save to the extent-explicitly otherwise stated that reproduction and publication thereof by Stellenbosch University will not infringe any third party rights and that I have not previously in its entirety or in part submitted it for obtaining any qualification.
2 abstract
The finite size of nucleons should play an important role in the description of high density nuclear matter as found in astrophysical objects. Yet we see that the Walecka model, which is generally used to describe these systems, treats the nucleons as point particles.
3 Here we argue that a non-commutative version of the Walecka model may be a consistent and appropriate framework to describe finite nucleon size objects. In this framework the length scale introduced through the non-commutative parameter plays the role of the finite 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.
4 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.
5 chapter one introduction

As a physicist one is blessed, or often cursed, with a very inquisitive nature to understand the world around them and comes up with various explanations of how nature orchestrates its existence. Some of these explanations have become known as laws of nature, while others still
remain simply as theories which are only able to describe a subset of physical situations or are only able to give approximations thereof. The theories of nuclear interactions are no exception.
As one of my prime interests in physics, nuclear interaction theories always seemed to be divided into two: The ones describing interactions at low energies or densities with no particle structure, and the theories describing interactions at high energies or densities with intrinsic structure.
6 As soon as one of these subsets of theories try to end a crossover to the other, many complications often arise which deems a theory unsolvable, or at least unsolvable with current technology.
As physicists are also ever searching, small improvements in technology and techniques within physics are made. This thesis will also be such an attempt into improving a technique of describing nuclear interactions dependent on the finite nucleon size. We outline the process of this research first by giving the aims of the thesis we want to reach.
7 1 1 Aims of this Thesis
It is common knowledge within modern physics that particles on the nuclear scale have finite size and plays a significant role in nuclear interactions. These particles on the nuclear scale, specifically baryons (or nucleons) and mesons, have been used in interaction theories, such as the Walecka model 1.
8 However, the Walecka model did not contain any information of the finite size of particles, but the particles are all described as point-like particles. This approach of point-like particles gives good quantitative results at low nuclear densities where nucleon size plays a minimal role, but this may not be the case at higher nuclear densities, such as astro-physical objects like Neutron Stars, where nucleon size may be an important factor.
9 We may turn to QCD which is a theory that already describes baryon interactions with finite baryon size and internal structure. However, QCD is a complicated and very involved theory, which becomes particularly difficult to solve at low energies. We therefore seek to introduce some kind of length scale or size to baryons using the much simpler Walecka model as a basis.
10 It is well-known that the introduction of finite sized objects in quantum field theory, or for that matter in any relativistic theory is plagued by inconsistencies. For example, if one would consider baryons as rigid bodies, it would be clear that an interaction on nuclear scale containing rigid bodies would violate causality since all points on the rigid body, which are spatially removed, would move at the same time during an interaction.
 

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