Quantization of waves: the stretched string

2021 ◽  
pp. 404-416
Author(s):  
Geoffrey Brooker
Keyword(s):  
Three Dimensions ◽  
One Dimension ◽  
Lagrangian Mechanics ◽  
Matrix Elements ◽  
Quantization Procedure ◽  
Raising And Lowering Operators ◽  
The Waves ◽  
Lowering Operators ◽  
Classical Lagrangian

“Quantization of waves: the stretched string” discusses waves in one dimension, in order to display the quantization procedure without the complication of three dimensions and of two polarization possibilities. Quantization goes via classical Lagrangian mechanics. The waves travel in both directions along the string, and we face up to disentangling these. The quantization procedure yields raising and lowering operators, their commutation rules, and their matrix elements.

The SU(2) realization for the Morse potential and its coherent states

2002 ◽  
Vol 80 (2) ◽  
pp. 129-139 ◽  
Author(s):  
S -H Dong
Keyword(s):  
Coherent States ◽  
Morse Potential ◽  
Transition Probability ◽  
Matrix Elements ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
The Matrix ◽  
Harmonic Perturbation ◽  
Analytical Expressions ◽  
Lowering Operators

A realization of the raising and lowering operators for the Morse potential is presented. We show that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are derived for the matrix elements of different functions such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied. The transition probability between two eigenstates produced by a harmonic perturbation as a function of the operators [Formula: see text]±,0 is discussed. The average values of some observables in the coherent states |α > for the Morse potential are also calculated. PACS Nos.: 02.30+b, 03.65Fd, 42.50Ar, and 33.10Cs

De kansen op conflict, mobilisatie en actie in een separatistisch proces

Res Publica ◽  
1986 ◽  
Vol 28 (1) ◽  
pp. 55-73
Author(s):  
Liesbeth Hooghe
Keyword(s):  
Collective Action ◽  
Social Economic ◽  
Three Dimensions ◽  
One Dimension ◽  
Central Idea ◽  
Political Opportunities ◽  
The People ◽  
The Social ◽  
Societal Changes ◽  
The Waves

A scheme of analysis for separatism is proposed. Its purpose is twofold: to indicate the essential factors in a separatist process, and to explain the waves of active and « dead » separatist activity.The central idea is the distinction between three dimensions in the separatist process : conflict, mobilization and collective action. Both dimension on its own is determined by certain factors. Conflict depends on contradictions of identity and interest structure between people and nation. Mobilization is primarily a function of the social, economic and political opportunities of the people as against the nation. Collective action is the result of the presence, strength and behaviour of the elite and social movement in people and nation.Evolution from one dimension to the next one depends upon the factors of the dimensions involved and on a) the policy of the nation (and perhaps the people) and b) the societal changes caused by the modernization process.Finally one can explain inactive and active periods by verifying the presence or absence of these nine factors. It seems then that there are false and real « dead » periods, and that some separatist activity has a sound basis white other has not.

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1867-1873 ◽  
Author(s):  
CHENG-MING BAI ◽  
MO-LIN GE ◽  
KANG XUE
Keyword(s):  
Representation Theory ◽  
Algebraic Structure ◽  
Zeeman Effect ◽  
Tensor Space ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
Degenerate States ◽  
Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

scholarly journals A demonstration that electroweak theory can violate parity automatically (leptonic case)

2018 ◽  
Vol 33 (04) ◽  
pp. 1830005 ◽  
Author(s):  
C. Furey
Keyword(s):  
Clifford Algebra ◽  
Ad Hoc ◽  
Higgs Bosons ◽  
Electroweak Theory ◽  
Ladder Operators ◽  
Raising And Lowering Operators ◽  
Ladder Operator ◽  
Left And Right ◽  
Electroweak Model ◽  
Lowering Operators

We bring to light an electroweak model which has been reappearing in the literature under various guises.[Formula: see text] In this model, weak isospin is shown to act automatically on states of only a single chirality (left). This is achieved by building the model exclusively from the raising and lowering operators of the Clifford algebra [Formula: see text]. That is, states constructed from these ladder operators mimic the behaviour of left- and right-handed electrons and neutrinos under unitary ladder operator symmetry. This ladder operator symmetry is found to be generated uniquely by [Formula: see text] and [Formula: see text]. Crucially, the model demonstrates how parity can be maximally violated, without the usual step of introducing extra gauge and extra Higgs bosons, or ad hoc projectors.

Conclusion

2020 ◽  
pp. 224-232
Author(s):  
Aleida Assmann
Keyword(s):  
Temporal Structure ◽  
Three Dimensions ◽  
One Dimension ◽  
Modern Time ◽  
The Past ◽  
The Future ◽  
Time Regime

This concluding chapter poses the question of whether or not we have too much past and too little future. After all, the notion of the past has dramatically increased in its range of meanings, as has the future. The relation between the past, the present, and the future is a three-fold relationship in which one dimension cannot exist for long without the others. Ordering this three-fold temporal structure anew and bringing the three dimensions into a balanced relation, however, continues to be an open adventure. To be sure, it is also the greatest challenge posed by the demise of the modern time regime.

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