دانلود کتاب ماهیت فرکتالی وحشی فضازمان گرانش کوانتومی هموار و کیهان‌شناسی

Thank you for picking up this, my third, book. Whatever may be your reasons for doing so, I would like to give you an introduction and overview of this monograph: In the spring of 1991, I studied physics in my second semester at Humboldt University of Berlin. During this time, I attended my first lecture on topology. The lecture was especially conceptualized for physics students and motivated the usage of topology in physics. This is where I, for the first time, learned of differential structures and their special role in relation to 4-dimensional manifolds: In every other dimension there are at most a finite number of varying differential structures, except for 4-dimensional spaces, where an infinite amount of differential structures are possible! Even the simplest space (the good old R4) carries uncountable infinitely different differential structures. The realization that this makes the fourth dimension superior to all other dimensions hit me in that moment. And I was determined to study and understand this theory! Regrettably, the common term Exotic Smoothness is chosen poorly in a way and suggests that the exotic differential structures are something particular and unimportant. But quite the contrary, the differential structure is the closest possible generalization of geometry, in the spirit of Einstein, who searched for exact generalization like those. Back then, the following concept started forming in my head: start with a fixed differential structure, consider the source-free Einstein equation and change the differential structure. Then, there should occur a source term in the Einstein equation or matter as source of the gravitational field is a result of the differential structure. This thought turned out to be some sort of leitmotif for my further work, even though I felt like the implementation of the associated mathematical problems were nearly insurmountable. Near the end of 1992, the first work by Carl H. Brans and Duane Randall on physical effects of differential structures was being published. I felt immensely inspired by his work. Finally, via detours, I would meet Carl personally in September 1995 and we started working together. A dream came true for me, as I had wanted to meet Carl since I was 12 years old, living behind the Iron Curtain, that separated half of Europe from the rest of the world. Back then, it would have been impossible to even seriously consider traveling, let alone go to America. I have talked about this in depth in my book “At the Frontier of Spacetime” (page xxiv). In 1998, following Carl’s invitation, I took a plane to New Orleans and together we developed the idea to our book writing project Exotic Smoothness and Physics. Only nine years later, in 2007, it was done: the first introduction into the theory of differential structures. Through working on this project, my line of research changed. I realized that a change in differential structures is unnecessary and needs a 5-dimensional manifold (a cobordism between both 4-dimensional manifolds). I repeatedly asked myself: How do the topologically similar boundaries (i.e. 3-dimensional manifold) of a 4-dimensional manifold with varying differential structure differ from each other? The 3-dimensional manifolds are characterized through a unique differential structure. But there must be a difference. In regard of this problem, I got the idea, that this difference is exactly what the theory of foliation for three-manifolds describes. It quickly became clear to me that these foliations (with the help of noncommutative geometry) represent an important bridge to quantum physics. This book aims to describe the path of differential structures to foliations of Spacetime and the depiction of exotic differential structures as sequence of topological changes of the space. The main conclusion of the book can be summarized as the following: a change in differential structures to an exotic differential structure can be understood as a quantization. Whereby the quantum states are wild, embedded three-manifolds. But how does the theory contextualizes itself in the current state of research?