Deformed special relativity and deformed symmetries in a canonical framework
Deformed special relativity and deformed symmetries in a canonical framework
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DOI：
10.1103/physrevd.75.105021
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发表时间：
2007-02
影响因子：
5
通讯作者：
S. Ghosh;Probir Pal
中科院分区：
文献类型：
--
作者：
S. Ghosh;Probir Pal
本文从正则相空间的角度研究了$\ensuremath{\kappa}$-Minkowski时空中运动学和动力学定律的性质。我们讨论了$\ensuremath{\kappa}$-Minkowski相空间代数的一种特殊形式，它产生了[D]中导出的$\ensuremath{\kappa}$-扩展有限Lorentz变换。Kimberly，J. Magueijo和J. Medeiros，Phys.Rev.D70，084007（2004）.]。这是变形狭义相对论模型的一种特殊形式，它允许修正的能量-动量色散定律以及非对易的$\ensuremath{\kappa}$-Minkowski相空间。我们表明，这个系统可以完全映射到一组相空间变量，服从正则（而不是$\ensuremath{\kappa}$-Minkowski）相空间代数和狭义相对论洛伦兹变换（而不是$\ensuremath{\kappa}$-扩展洛伦兹变换）。构造了一套完整的变形对称生成元，它服从一个未修改的闭代数，但在物理$\ensuremath{\kappa}$-Minkowski相空间变量的对称变换中引起变形.此外，我们证明了这种方法的实用性和简单性，通过一些现象学的应用在经典和量子力学。我们还为$\ensuremath{\kappa}$-粒子构造了一个拉格朗日量。
In this paper we have studied the nature of kinematical and dynamical laws in $\ensuremath{\kappa}$-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $\ensuremath{\kappa}$-Minkowski phase space algebra that yields the $\ensuremath{\kappa}$-extended finite Lorentz transformations derived in [D. Kimberly, J. Magueijo, and J. Medeiros, Phys. Rev. D 70, 084007 (2004).]. This is a particular form of a deformed special relativity model that admits a modified energy-momentum dispersion law as well as noncommutative $\ensuremath{\kappa}$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not $\ensuremath{\kappa}$-Minkowski) phase space algebra and special relativity Lorentz transformation (and not $\ensuremath{\kappa}$-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical $\ensuremath{\kappa}$-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the $\ensuremath{\kappa}$-particle.