Super-Symmetry

Dear Colleagues,

Supersymmetry is the symmetry between fermionic states and bosonic states. In 1973, J. Wess and B. Zumino presented an analytical 4-dimensional gauge theory that preserves supersymmetry.

In 1981, in his article Supersymmetry at ordinary energies. Masses and conservation laws, S. Weinberg presented a violation of supersymmetry in the Standard Model of elementary particles, whereby the anomaly cancels when there are three generations of quarks and gluons. In 1984, Fubini and Rabinovici presented a model of superconformal quantum mechanics, in which spontaneous symmetry breaking occurs.

Mesons consist of quarks and antiquarks, and the main hadrons consist of three quarks. S.J. Brodsky and his group HLFHS (Holographic Light-Front Hadron Study) showed that the supersymmetric spectra can be obtained by choosing hadron wavefunctions in the front form. The light-front effective Hamiltonians of bosons and fermions are different due to the spin dependence of the latter. There are mathematical formulae that justify their approach to obtaining global solutions from local analytic solutions.

A comprehensive theoretical review of the supersymmetry of elementary particles is given in the book of P. Labelle (2010). 

At CERN, the CMS-ATLAS group and other groups study the violation of supersymmetry which can be attributed to couplings of the Higgs boson and fermions. At Jefferson laboratory, quark distribution functions in mesons and baryons are being studied.

In 1983, K.B. Efetov presented theoretical studies of the motion of an electron in a disordered system, based on generating functionals and creation and annihilation operators. In the case of bosons, integral on commuting variables was done, while in case of fermions, integral on a Glassmann algebra G_n was used, which is connected with the Clifford spinor algebra K_2n-. The method was applied to a study of normal-superconducting hybrid structures by A. Altrand and M. Zirnbauer in 1996, and a review of application of the supersymmetry in solid state physics is given in a book of Efetov (1997).

The propagation and scattering of phonetic waves in media is also well described by front form. The effects of noise are expected to be taken into account in the framework of supersymmetry.

In this book we aim to present an aspect of supersymmetry biased by an Editor's interest, and we would be grateful if you sent your suggestions or references relevant to the above subjects to the editor.

[1] J. Wess and B. Zumino, Supergauge Transformation in Four Dimension, Nucl. Phys. 39-50 (1974).

[2] S. Weinberg, Supersymmetry at ordinary energies. Masses and conservation laws, Phys. Rev. (10) 287-302 (1982).

[3] S. Fubini and E. Rabinovici, Superconformal Quantum Mechanics, Nucl. Phys. 17-44 (1984).

[4] Patrick Labelle, Supersymmetry Demystified, McGraw-Hill Comp., (2010).

[5] K.B. Efetov, Supersymmetry and theory of disordered metals, Advances in Physics, (1) 53-127 (1983).

[6] F.A. Berezin, The Method of Second Quantization, Translated to English by N. Mugibayashi and A. Jeffrey, Academic Press, New York and London, (1966).

[7] A. Altrand and M. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. (2) 1142-1161 (1997).

[8] Konstantin Efetov, Supersymmetry in Disorder and Chaos, Cambridge University Press (1997).

Prof. Dr. Sadataka Furui
Guest Editor

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