**Author details**

symmetry it is equal to 10). In case of the simple irreducible representation (IR) the number of collective modes is equal to twice number of irreducible representation dimensionality. For orthorhombic (OR) symmetry and singlet pairing all irreducible representations are one dimensional (1D), so in each superconducting state there are two modes corresponding to phase and amplitude variations. Amplitude mode is high frequency with *E*≈2Δ, where Δ is the gap in a single particle spectrum. Among irreducible representations of tetragonal (TG) symmetry there are 1D as

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

superconducting states, with two collective modes of conventional superconductors there are states which have four collective modes, none of which are Goldstone. We would like to mention, that for cylindrical Fermi–surface (*D*∞) among collective modes there is Goldstone mode in 1, 0 ð Þ and 1, 1 ð Þ states but there is not Goldstone

Because it looks like that there is a mixture of different irreducible representations (corresponding, for example, to *s*– and *d*–wave states or to two different *d*– wave states: *dx*<sup>2</sup>�*y*<sup>2</sup> and *dxy*; or *dxz* and *dyz*) it will be interesting to investigate the collective mode spectrum in this case for different admixture values of *s*–wave state (*dxy*– state). Considered by Brusov et al. particular case of *dx*<sup>2</sup>�*y*<sup>2</sup> þ *idxy* state [1] shows that such consideration leads to very interesting results. One more possibility is connected with the recent experiments in Sr2RuO4 where the p–pairing appears to have been precluded by recent NMR experiments, the two–component d–wave order parameters, namely {dxz,dyz} and even with admixture of g–wave {dx2�y2, gxy(x2�y2}, are now the prime candidates for the order parameter of the quasi–two– dimensional Sr2RuO4. So, it will be interesting to study the collective mode spec-

We consider all superconducting states, arising in symmetry classification of p-wave and d-wave 2D–superconductors, and calculate the full collective modes

The collective mode spectrum could manifest itself in microwave impedance technique, in ultrasound experiments, ultrasound velocity measurements and others. They allow determine the type of pairing and the symmetry of order

2D (remind that we consider the singlet pairing). Thus in addition to the

mode in 1, ð Þ*i* state.

trum in such states.

**5. Conclusions**

**74**

spectrum for each of these states.

parameter in HTSC and HFSC.

Peter Brusov<sup>1</sup> \* and Tatiana Filatova<sup>2</sup>

1 Department of Mathematics, Financial University under the Government of Russian Federation, Moscow, Russia

2 Department of Financial and Investment Management, Financial University under the Government of Russian Federation, Moscow, Russia

\*Address all correspondence to: pnb1983@yahoo.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
