A Clifford algebra quantization of Dirac's electron positron field

淡江大學機構典藏 > 理學院 > 物理學系暨研究所 > 期刊論文 > Item 987654321/27594

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题名:	A Clifford algebra quantization of Dirac's electron positron field
作者:	曹慶堂;Cho, H. T.;Diek, Adel;Kantowski, R.
贡献者:	淡江大學物理學系
日期:	1990-09
上传时间:	2009-12-31 10:28:16 (UTC+8)
出版者:	American Institute of Physics (AIP)
摘要:	The quantum field theory of free Dirac particles (four‐component massive spin‐ 1/2 particles) is ‘‘derived’’ by a Segal quantization procedure. First, details are given on how the spinor space of Dirac is actually a minimal left ideal of the Clifford algebra associated with a Lorentz inner product space (+,−,−,−), and how the homogeneous group actions break the natural two‐component quaternion structure to give familiar four‐component complex spinors. Second, Wigner’s procedure for constructing unitary representations of the Poincaré group is used to construct the appropriately induced infinite‐dimensional representation of the inhomogeneous group starting from the above four‐dimensional nonunitary representation. Third, and finally, Segal’s procedure for quantizing classical Fermion fields is adapted to this infinite‐dimensional Hilbert space to obtain the Clifford algebra of annihilation–creation operators for spin‐ 1/2 particles. The familiar Fock space appears as a minimal left ideal in this second Clifford algebra.
關聯:	Journal of mathematical physics 31(9), pp.2192-2200
DOI:	10.1063/1.528623
显示于类别:	[物理學系暨研究所] 期刊論文

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