Supersymmetry

The structure of the system (125) is very special. It is again a system of two ordinary differential equations, but the coupling between u and v is now rather simple. Iterating the system immedately leads to the two equations 

Conversely, solutions of these second order equations determine solutions of the system (125) according to the following observation, which is the basic observatioin of supersymmetric quantum theory  

On the other hand, once we have found an eigenvalue A and a solution v of (129), such that D v 0, then D v is a solution of the equation (128). Moreover, 

What do we get, if, for example, D v = 01 The considerations above tell us nothing about the solutions of the equation (128). But we can learn something from the matrix equation (131). Inserting D v = Owe obtain the following two equations  

So either we have n = 0 and A = —fi, or we have u =4 0, and hence = fi. If we assume that u were nonzero, we would find from the second equation that Du = 2fj,v and hence Du = 2piD v = 0. One can show that D Du = 0 is equivalent to Du = 0. This in turn would imply A = —ju which is a contradiction to the assumption u O. So the only possiblity is that u = 0. Let us state this clearly  

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Table I presents the estimate of the electron EDM predicted by different particle physics models [8, 9]. As can be seen from this table, the value of the electron EDM in the SM is 10-12 orders of magnitude smaller than in the other models. This is due to the fact that the first nonvanishing contribution to this quantity arises from three-loop diagrams [30]. There are strong cancellations between diagrams at the one-loop as well as two-loop levels. It is indeed significant that the electron EDM is sensitive to a variety of extensions of the SM including supersymmetry (SUSY), multi-Higgs, left-right symmetry, lepton...

Supersymmetry (SUSY), electron electric dipole moment, particle physics implications, 242-243... 

N.J. Hitchin, A. Karlhede, U. Lindstrom and M. Rocek, Hyperkdhler metrics and supersymmetry. Comm. Math. Phys. 108 (1987), 535-589. 

Kazakov, D. I. Beyond the standard model (In search of supersymmetry) 2000. ArXiv hep-ph/0012288. 

Mohapatra, R. N. Unification and Supersymmetry. The Frontiers of Quark-Lepton Physics (Springer, New-York, U.S.A., 2003). 421pp. 

The connection between the potentials V and W is called the Darboux transforma-tion ) or supersymmetry ... 

Supersymmetry will be investigated, and may lead to unified field theories llidt include gravity,... 

Ellis, J Hope Grows for Supersymmetry, Nature, 313(6004), 626-627 (February... 

Haber, H.E. and G.L. Kane The Search for Supersymmetry Probing Physics Beyond the Standard Model, Physics Reports, 117(2, 3), 75 263 (January 1985). Haber, H.E. and G.L Kane Is Nature Supersymmetric Sci. Amer., 52-60 (June... 

The research interests of Rod Truax fall under the general heading of symmetry and supersymmetry and their applications to problems of chemical and physical interest. He is especially interested in finding the symmetry associated with time-dependent models and exploiting this symmetry to compute solutions to the quantum mechanical equations of motion. 

Recent developments in applications of supersymmetry to the study of complex spectra are discussed. In particular, extensions of supersymmetry to nuclei with an odd number of protons and neutrons are presented. 

The concept of supersymmetry in nuclei has been extended in the last year to include the proton-neutron degree of freedom [HUB85,VAN85 ]. With this extension, it becomes possible now to predict prperties of odd-odd nuclei. Thus, in addition to providing the first experimental example of supersymmetry in physics [CAS84,1AC85], this concept appears now to be able to make predictions for yet unknown quantities. The experimental determination of the predicted spectra will indicate to what extent supersymmetry is useful in nuclear physics. 

I wish to thank V. Paar, P. van Isacker, and A. Frank for pointing out the importance of supersymmetry in odd-odd nuclei and A.B. Balantekin and I. Bars for many discussions on the subject. This work was performed in part under DOE Contract No. DE-AC-02-76-ER-03074. 

Boson-Fermion Symmetries and Dynamical Supersymmetries for Odd-Odd Nuclei... 

The concept of boson-fermion symmetries and supersymmetries is applied to odd-odd nuclei. 

Here we discuss the boson-fermion system for odd-odd nuclei using the concept of dynamical symmetry and supersymmetry. The dimension of the fermionic subspace is nv, where n- (nv) is the total number of compo-... 

The concept of dynamical supersymmetries was successfully used to connect the properties of even-even nuclei with the neighboring odd-even nuclei. If we want to study, say, the correlation between an even-even nucleus and the next, odd-proton nucleus, the first decomposition in the supergroup chain is... 

As an illustration of dynamical supersymmetry with canonical decomposition we construct a supermultiplet starting from the even-even nucleus 194Pt. In this region the proton shell is dominated by j = 3/2 and the neutron shell by j = 1/2,3/2,5/2. Hence n = 4 and n =12. The relevant representation of the appropriate supergroup U(6/16) is the one with Jf= 7. Various nuclei are placed in the tensor product representations as follows ... 

A new possibility of supersymmetry arises when n = nv = n. In this case, using fermionic creation and annihilation operators it is possible to construct the generators of the symplectic group Usp (2n). Consequently a supergroup chain starting with decomposition into the orthosymplectic group U (6/2n) Osp (6/2n) (7)... 

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