title: Matrix operator symmetries of the Dirac equation and separation of variables

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].

text: Matrix operator symmetries of the Dirac equation and separation of variables The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].

year: 1986-07

title: "The manliest and noblest of all pursuits and professions": Two preacher novelists

authors: Moffat, Kirstine

abstract: The secular character of New Zealand has become an accepted `facts of our time. Nevertheless, Christian organizations and discourses have played an important role in framing New Zealand's life and identity.

text: "The manliest and noblest of all pursuits and professions": Two preacher novelists The secular character of New Zealand has become an accepted `facts of our time. Nevertheless, Christian organizations and discourses have played an important role in framing New Zealand's life and identity.

year: 2016

title: Ngā Pakanga mō Wāhi Tapu: Battles over sacred places

authors: Joseph, Robert

abstract: Wāhi tapu are the sacred places of Māori in Aotearoa New Zealand. All cultures have sacred sites such as cemeteries, significant battlefields, and places of spiritual significance. Standout examples internationally include the ‘Weeping Wall’ in the Holy Land, Stonehenge in Britain, Maraeātea in the Pacific, and Intihuatana at Macchu Picchu in Peru. But unlike these sites, wāhi tapu are rarely a visible structure but rather a site or area within the landscape with values so significant that restrictions are warranted. In law, wāhi tapu are defined as a ‘place of special significance according to tikanga Māori’
 and ‘a place sacred to Māori in the traditional, spiritual, religious, ritual, or mythological sense’.
As the aphorism above emphasises, Māori historically were willing to die for land (and for women of course!), and wāhi tapu are the most sacred of places. Many battles have been fought over actual or proposed transgressions of their sacredness. In earlier years, blood was shed and men did die; today battles tend to occur in the Environment Court, but are just as passionate. Recent decades have seen conflicts where wāhi tapu were threatened by new highways, railroads, airports, prisons, residential and commercial developments, wind farms, power stations and waste dumps.
In this chapter, I discuss a number of the battles that have been fought over the development or preservation of wāhi tapu from first European contact up until the present time. I highlight the growing legal recognition of tikanga Māori in relation to these sacred landscapes, and conclude with a proposed pragmatic solution for all New Zealanders when negotiating developments over wāhi tapu. Having a
background in law and tribal affiliations, I discuss these tensions from both legal and kaupapa Māori perspectives.

text: Ngā Pakanga mō Wāhi Tapu: Battles over sacred places Wāhi tapu are the sacred places of Māori in Aotearoa New Zealand. All cultures have sacred sites such as cemeteries, significant battlefields, and places of spiritual significance. Standout examples internationally include the ‘Weeping Wall’ in the Holy Land, Stonehenge in Britain, Maraeātea in the Pacific, and Intihuatana at Macchu Picchu in Peru. But unlike these sites, wāhi tapu are rarely a visible structure but rather a site or area within the landscape with values so significant that restrictions are warranted. In law, wāhi tapu are defined as a ‘place of special significance according to tikanga Māori’
 and ‘a place sacred to Māori in the traditional, spiritual, religious, ritual, or mythological sense’.
As the aphorism above emphasises, Māori historically were willing to die for land (and for women of course!), and wāhi tapu are the most sacred of places. Many battles have been fought over actual or proposed transgressions of their sacredness. In earlier years, blood was shed and men did die; today battles tend to occur in the Environment Court, but are just as passionate. Recent decades have seen conflicts where wāhi tapu were threatened by new highways, railroads, airports, prisons, residential and commercial developments, wind farms, power stations and waste dumps.
In this chapter, I discuss a number of the battles that have been fought over the development or preservation of wāhi tapu from first European contact up until the present time. I highlight the growing legal recognition of tikanga Māori in relation to these sacred landscapes, and conclude with a proposed pragmatic solution for all New Zealanders when negotiating developments over wāhi tapu. Having a
background in law and tribal affiliations, I discuss these tensions from both legal and kaupapa Māori perspectives.

year: 2011