کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5495820 | 1529826 | 2017 | 39 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A representation of Weyl-Heisenberg Lie algebra in the quaternionic setting
ترجمه فارسی عنوان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
فیزیک و نجوم
فیزیک و نجوم (عمومی)
چکیده انگلیسی
Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the so-obtained position and momentum operators, we study the Heisenberg uncertainty principle on the whole set of quaternions and on a quaternionic slice, namely on a copy of the complex plane inside the quaternions. For the quaternionic harmonic oscillator, the uncertainty relation is shown to saturate on a neighborhood of the origin in the case we consider the whole set of quaternions, while it is saturated on the whole slice in the case we take the slice-wise approach. In analogy with the complex Weyl-Heisenberg Lie algebra, Lie algebraic structures are developed for the quaternionic case. Finally, we introduce a quaternionic displacement operator which is square integrable, irreducible and unitary, and we study its properties.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 385, October 2017, Pages 180-213
Journal: Annals of Physics - Volume 385, October 2017, Pages 180-213
نویسندگان
B. Muraleetharan, K. Thirulogasanthar, I. Sabadini,