Название: Supersymmetry and Superstring Theory with Engineering Applications
Автор: Harish Parthasarathy
Издательство: CRC Press
Год: 2023
Страниц: 198
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

This book gives the reader an introduction to the vast subject of supersymmetry along with many examples having engineering applications like the design of quantum unitary gates using supersymmetric actions, Bosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculus, superstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can for example be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding it. Simplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introduced. All through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.

The intricacies involved in understanding the calculus of Bosonic and Fermionic variables and supervector fields as representations of the Boson-Fermion super-algebra, are clearly explained including facts like how supersymmetry predicts that the mass of the Dirac electron should depend upon the Bosonic scalar field.

Local supersymmetry has been discussed in the context of superparticles, superstrings and super-gravity. In local supersymmetry, the action is invariant even when the Majorana Fermionic parameter appearing in the definition of a supersymmetry transformation becomes a function of the space-time variables. Thus, if nature really follows local supersymmetry then our quantum gates designed based on such Lagrangians using the Feynman path integral for fields would have nice symmetry properties.

It is hoped that with this introduction, the reader will be able to understand some more important problems involving supersymmetry breaking at high energy scales and how this is communicated to lower energy scales via messenger superfields or by gravitational fields which is the reason why so far superpartners of the particles in the standard model are yet to be observed in particle accelerators. If superpartners of elementary particles are detected at higher energy scales where supersymmetry is unbroken, then it would provide the engineer the opportunity to design quantum gates for computers by operating at higher energies.

This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example:

• The design of quantum unitary gates using supersymmetric actions.
• Bosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculus.
• Superstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding it.
• Simplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introduced.