Quantum Statistics of Identical Particle System Inside A Topologically Changing Space  

Oleh:

Bama, Akhmad Aminuddin ; Muslima ; Rosyid, M.F. ; Satriawan, Mirza

Jenis: Article from Journal - ilmiah nasional - tidak terakreditasi DIKTI
Dalam koleksi: SIGMA: Jurnal Sains dan teknologi vol. 11 no. 1 (Jan. 2008), page 19-30.
Topik: Inequivalent Quantizations; Quantum Statistics; Topology Change; History-Like

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: SS25.6 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

An investigation is carried out on inequivalent quantizations and statistics for a quantum mechanical system of identical particles occupying a topological space-time M undergoing spatial topology changes. In this paper, a new concept has been introduced related to the construction of inequivalent quantizations for a system, which is called “history-like path” for particles. This is a collection of non-causal homotopical paths. Each homotopy class of paths will be labelled with a “word” constructed from the generators of fundamental group ..7r1(QN(_~)) of a configuration space of the system in a space-like which is a deformation retract of M1 region that is a sub-space-time of M in which there is no singular slice (a slice M~ in M that contains a singular point). The labels determine the generators and their relations in constructing the fundamental group 2r1(QN) of the system. By using the new concept, two methods are proposed to construct inequivalent quantizations of a system of identical particles undergoing a spatial topology change, either via a ‘local-local” (L-L) or a “global-local” (G-L) quantization. The first method corresponds to constructions of inequivalent quantizations of the system in each region M, in M. Each of them is in a (1-1)-correspondence with irreducible unitary representations (IUR’s) of a fundamental group ..‘r1(QN(~) BN(~) constructed by generators in each of the regions corresponding to the possible history-like homotopy paths. A possible statistics for N-identical particles in M is determined by a sub-representation of IUR of braid group BN(1). The sub-representation is a representation of a subgroup fN(2~) which is a subgroup of BN(~) only generated by permutation of particles. The second method is based on a construction of inequivalent quantizations of the system in M. They are in the (1-1)-correspondence with IUR’s of the fundamental group .‘z~1(QN(~)) BN(’~) raised by generators corresponding to the history-like homotopical paths of the system in M; and these inequivalent quantizations are considered valid for all regions M1 in M. A possible statistics for N-identical particles in M is determined by a sub¬representation of IUR of braid group BN(2), i.e. a representation of rN(~) CBN(~).

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