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COBIT is a framework and supporting toolset that allow managers to bridge the gap with respect to control requirements, technical issues and business risks, and communicate that level of control to stakeholders COBIT enables the development of clear policy and good practice for IT control throughout enterprises COBIT is continuously kept up to date and harmonised with other standards Hence, COBIT has become the integrator for IT best practices and the umbrella framework for IT governance that helps in understanding and managing the risks and benefits associated with IT The process structure of COBIT and its high-level business-oriented approach provide an end-to-end view of IT and the decisions to be made about IT The benefits of implementing COBIT as a governance framework over IT include: Better alignment, based on a business focus A view, understandable to management, of what IT does Clear ownership and responsibilities, based on process orientation General acceptability with third parties and regulators Shared understanding amongst all stakeholders, based on a common language Fulfillment of the COSO requirements for the IT control environment The rest of this document provides a description of the COBIT framework, and all of the core COBIT components organised by COBIT s IT domains and 34 IT processes This provides a handy reference book for all of the main COBIT guidance Several appendices are also provided as useful references Implementation is supported by a number of ISACA/ITGI products including online tools, implementation guides, reference guides and educational materials The latest information on these products can be found at wwwisacaorg/cobit

Any system having such commutation rules has the group SU (2) as a dynamical group, that is, a group whose elements connect states with different energies

Coherent States in Quantum Physics Jean-Pierre Gazeau Copyright 2009 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40709-5

Figure 13: (continued)

The generators of this group are in the present context [2]{a , a, a a 1/2}, with the commutation rules [a , a] = 2 a a

(112)

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It is important to note that these commutation rules are derived from the anticommutation rules (111) and not from the usual canonical commutation rules Let us now proceed to the construction of the corresponding coherent states 2 Since a = 0 = a 2 , the only pertinent Hermitian space is the two-dimensional ~ Hermitian one, H j =1/2 = C2 Thus, it is enough to repeat the construction of the 2 standard coherent states, but keeping the constraint a = 0 = a 2 , or the construction of the SU (2) coherent states with spin generators J and j = 1/2 Hence, we associate with C the states |

Source: 1996, 1998, 2000, 2005 IT Governance Institute (ITGI) All rights reserved Used by permission

| ,

(113)

where | (= | 1 1 in SU (2) notation) are such that a | = |+ , a|+ = | Since 2 2 ( a a)2 = | |2 (a a + aa ) = | |2 , we have e Putting |

|+ + sin e i | , 2 2

important second set of values: that of a challenger brand ghting for superior value against the big boys like BA Direct stretching added Virgin Holidays in 1985 By the end of the 1980s, the Virgin brand was no longer an entertainment business or a pioneering and challenging airline business, but somehow a mix of the two One way of trying to sum this up is the idea of Virgin being an irreverent, fun-loving ghter for value The 1990s saw the launch of Virgin s many extensions, which we have now come to associate with the brand (Figure 13)

Source: 1996, 1998, 2000, 2005 IT Governance Institute (ITGI) All rights reserved Used by permission

i e |+ + cos | , 2 2

(114)

in which we recognize the spin or Bloch coherent states for j = 1/2 Therefore, we inherit the properties of spin coherent states in the present fermionic context, like the overlap relation (631), the way they behave under the action of an SU (2) transformation (628), and the resolution of the identity (610) Note that we could also use the other complex parameterization = tan e i , a notation that we will 2 recover on a more general level in the next sections

113 Coherent States for Systems of Identical Fermions 1131 Fermionic Symmetry SU(r)

.

We now consider a system of r fermionic states or modes occupied by at most one fermion To each mode corresponds one pair (a , a i ) of operators obeying the i anticommutation rules (111): [a i , a j ]+ = i j , [a i , a j ]+ = 0 = [a , a j ]+ , i 1 u i, j u r (115)

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