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arXiv:hep-th/0106216 · Journal of High Energy Physics

Quantum determinism for free vector bosons in 3 dimensions

Philippe Pouliot

Published Nov 14, 2001• 1 citation
arXivHTMLPDF
DOI
10.1088/1126-6708/2001/11/028

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In the construction and classification of the possible state vectors of a limited number of boson modes, the use of subalgebras of invariant operators can simplify the procedure. The subalgebra of all the invariant operators (invariant subalgebra) and the subalgebra generated by the invariant-pair operators (invariant-pair subalgebra) are both considered. The invariant-pair subalgebra has the decisive advantage of allowing the easy evaluation of matrix elements. The construction problem is reduced to the problem of constructing the invariant-pair-free states, and a general procedure for determining these states is presented.
By extending local U(1) gauge symmetry to discontinuous case, we find that under one special discontinuous U(1) gauge transformation the symmetric and antisymmetric wave functions can transform into each other in one dimensional quantum mechanics. The free spinless fermionic system and bosonic system with δδδ-type vector gauge potential are proved to be equivalent. The relation also holds in higher space-time dimensions.