Yakov M. Shnir Boeken

“One would be surprised if Nature had made no use of it.” P. A. M. Dirac. The concept of “beauty” often aligns with “symmetry,” suggesting that beauty may not solely be subjective but linked to the symmetry of objects. This idea is particularly appealing in physics, where the pursuit of higher symmetry has been central to theoretical advancements over the past two centuries. The more symmetric a theory, the more aesthetically pleasing it appears. However, our world is rife with broken symmetries, especially at low energy scales, prompting physicists to explore the mechanisms behind these violations and how symmetry might be restored, enhancing our understanding of Nature's beauty. A notable example of broken symmetry is the absence of magnetic monopoles, which disrupts the symmetry between electric and magnetic charges. The quest to regain this symmetry through the hypothesis of magnetic monopoles stands out in the history of theoretical physics. This unique theoretical construct has persisted for over a century without experimental evidence, yet it continues to inspire rigorous research among generations of physicists, making it a remarkable focal point in the field.

Focusing on scalar field models, this book explores both integrable and non-integrable systems, delving into the fascinating world of soliton solutions. It highlights the distinction between topological and non-topological solitons, providing insights into their mathematical foundations and physical implications. Through a structured approach, the text aims to enhance understanding of complex field theories and their applications in various scientific domains.