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Nano- and Microscale Systems, Devices, and Structures
Published in Sergey Edward Lyshevski, Nano- and Micro-Electromechanical Systems, 2018
In this book, we will utilize the so-called standard model (particles are considered to be points moving through space and coherently represented by mass, electric charge, interaction, spin, etc.), see Fig. 2.5. The standard model was developed within a quantum field theory paradigm that is consistent with quantum mechanics and the special theory of relativity. Electromagnetism and the strong and weak nuclear forces are integrated. However, the gravity (fourth interaction) from Einstein’s general relativity theory does not fit into quantum field theory. In fact, the quantum field theory and general relativity cannot be integrated. To overcome these limits, string theory has been developed. In string theory, instead of particles, one utilizes a fundamental building block called a string that can be closed (loop) or open. As the string moves through time, it traces out a tube (closed string) or a sheet (open string). The string is free to vibrate, and different vibration modes of the string represent the different particle types, since different modes are seen as different masses or spins. For example, modes of vibration (notes) may represent electrons or photons. String theory provides a consistent unified method that integrates electromagnetism, strong and weak nuclear forces, and gravity. The particles known in nature are classified according to their spin into bosons (integer spin) or fermions (odd half-integer spin). Examining the forces, we emphasize that the photon carries electromagnetic force, the gluon carries the strong nuclear force, and the graviton carries the gravitational force. Recently, superstrings and heterotic string theories have been introduced, and many other concepts have emerged. The unified paradigm is called the M-theory. We usually apply three dimensions of space and one of time. String theory utilizes 10-dimensional space and time. These extra dimensions, which can confuse the reader, could be unobservable, but compact dimensions result from mathematical deviations.
Geometric theory of topological defects: methodological developments and new trends
Published in Liquid Crystals Reviews, 2021
Sébastien Fumeron, Bertrand Berche, Fernando Moraes
A major contemporary challenge in physics is to find an extension of General Relativity able to describe gravity at all energy scales, in particular at the very beginning of the universe. This is the mission devoted to quantum gravity theories, which have the daunting task of reconciling Einstein's general relativity and quantum field theory. Despite promising attempts, including superstring theories, M-theory or quantum loop gravity, no proposal is entirely satisfactory up to now, and even so, the energy scales required to test these theories are far beyond our current scientific capabilities. A way out of this gridlock is to rely on simpler models that capture the essential features of quantum gravity but remain connected to low-energy-physics systems, i.e. analog gravity. The rare pearl was first introduced in a seminal paper by Deser, Jackiw and 't Hooft [141]: 2 + 1 gravity with point-particle sources.