When Diving Into The Details Of Gravitational Theories

Before diving into the details of gravitational theories with anisotropic scaling, we discuss some important ingredients of the theory and why they are essential. 2.1.1 Higher order terms The non-renormalizability of General Relativity means that it is an effective theory and the Einstein-Hilbert action contains only the terms relevant at low energies. Then one naturally is tempted to add higher order curvature terms to the action thereby making the theory applicable at high energies. This possibility was first explored in 1962 by R. Utiyama and Bryce S. DeWitt [33]. They noticed that the action of quan- tum gravity should contain functionals of higher derivatives of metric tensor besides the Einstein-Hilbert action. But is such a theory renormalizable? This question was answered in affirmitve in 1977 by Kellogg Stelle [34]. He showed that the theory is renomalizable with quadraditic curvature invariants. However due to the presence of higher time derivatives, such a theory has the negative norm state called ghosts which allow the probability to be negative and hence breaks the unitarity. In fact, as back as in 1850, Mikhail Ostrogradsky showed that presence of time d erivatives higher than two will lead to the problem of ghosts [35]. Combining all these ideas, Horava added only the terms containing higher spacial derivatives while keeping the time derivatives to second order. Also the power-counting renormalizability restricts the number of spatial derivatives to six. ThisShow MoreRelatedPhysics in Daily Life13985 Words   |  56 Pagesrequired will be simple and direct. When reference is made to particular situations or apparata which might be unfamiliar to candidates, sufficient details will be given to explain the context. Mathematical content The use of non-programmable electronic calculators with arithmetical (four rules, squares, square root, log) and simple trigonometrical functions (sin, cos, tan, and their inverses in degrees) is recommended. Standard notation and SI units will be used. When one quantity is divided by anotherRead MoreOrganisational Theory230255 Words   |  922 Pages. Organization Theory Challenges and Perspectives John McAuley, Joanne Duberley and Phil Johnson . This book is, to my knowledge, the most comprehensive and reliable guide to organisational theory currently available. What is needed is a text that will give a good idea of the breadth and complexity of this important subject, and this is precisely what McAuley, Duberley and Johnson have provided. They have done some sterling service in bringing together the very diverse strands of work