Schwinger's model of angular momentum with GUP

Abstract

We study the generalized uncertainty principle (GUP) modified simple harmonic oscillator (SHO) in the operator formalism by considering the appropriate form of the creation and annihilation operators A, A † . The angular momentum algebra is then constructed using Schwinger's model of angular momentum with two independent GUP modified SHOs. With the GUP modified angular momentum algebra, we discuss coupling of angular momentum for a two-particle composite system. Further, we calculate the Clebsch-Gordan (CG) coefficients for a two-particle system explicitly. Our results show that the CG coefficients do not receive any corrections upto quadratic GUP. p-7

Comments on "Schwinger's Model of Angular Momentum with GUP" by H. Verma et al, arXiv:1808.00766

“…The results of [1], therefore, still stand, and the objections raised in [2] are invalid. Nevertheless, it is possible that a correct application of the Jordan map to the GUP-modified angular momentum operators may be an useful tool in gaining insight into the problem in question and its possible resolution.…”

“…Verma et al, in [2], have tried a possible resolution of the above ambiguity. Below, we comment on the main aspects of their paper.…”

“…Notice that the expressions, used by Verma et al in [2], are constructed from the representation of the angular momentum operators as Pauli matrices. A property of the Jordan map is that it preserves commutation relations.…”

“…In other words, whatever the commutation relations for the angular momentum matrices are, the operators in terms of ladder operators will have the same relations, since they are inherited from the matrices. Notice therefore that (i) the procedure used in [2] is flawed, because their A, A : operators are not ladder operators, as explained above, (ii) tautological, as starting from a representation of the standard (non GUP) angular momentum algebra, the authors use the Jordan map to find the commutation relations for the angular momentum operators, which necessarily are the standard one.…”

“…Having this picture in mind, it is clear that the normalization of Clebsch-Gordan coefficients has to be performed considering the independent normalization of states |L, M y with different values M and the orthogonality among the states of equal M but different L. However, in [2] the authors seem to normalize states belonging to different values of M simultaneously, resulting in constraints such as…”