Realization Of Green Research Articles

T. H. Green's community of rights: an essay on the complexity of liberalism

It is a common communitarian and feminist criticism of liberalism that its preoccupation with rights is incompatible with and even hostile to the possibility of community. I claim that the inseparability of rights and community is a consistent liberal position. To that end, I explore Green's liberal argument. Though he places community at the heart of liberalism, this move is bound up with reconstructing the institution of rights which, in turn, is bound up with transforming some key liberal ideas, such as ‘interest’ and ‘state interference’. Transformed both in form and content, rights are constitutive of and are essential to the realization of Green's ideal of community. Indeed, community of rights is itself a common good. Though the explicit object of the article is to examine Green's liberal argument, my implicit goal is to indicate the complex nature of liberalism which is misconceived if we freeze it into a fixed conceptual basket of ideas.

Exclusion statistics, operator algebras and Fock space representations

We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.