Generalized quantum relativistic kinematics: A stability point of view

被引:60
作者
Chryssomalakos, C [1 ]
Okon, E [1 ]
机构
[1] Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Mexico City 04510, DF, Mexico
来源
INTERNATIONAL JOURNAL OF MODERN PHYSICS D | 2004年 / 13卷 / 10期
关键词
Poincare algebra deformations; deformed special relativity; non-commutative spacetime; Heisenberg algebra; invariant length scale; invariant mass scale;
D O I
10.1142/S0218271804006632
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes in on the Poincare-plus-Heisenberg algebra in about a minute. Further ahead, along the same path, lies a three-dimensional deformation space, with an instability double cone through its origin. We give physical as well as geometrical arguments supporting our view that moment, rather than position operators, should enter as generators in the Lie algebra. With this identification, the deformation parameters give rise to invariant length and mass scales. Moreover, standard quantum relativistic kinematics of massive, spinless particles corresponds to non-commuting moment operators, a purely quantum effect that bears no relation to spacetime non-commutativity, in sharp contrast to earlier interpretations.
引用
收藏
页码:2003 / 2034
页数:32
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