Foreword
This electronic lecture covers the theory of "quantum graph", which is one of the main subject under current research at the Mathematical Engineering Laboratory/ Theoretical Physics Group at Kochi University of Technology.
The lecture is based on various review articles by the author which have appeared on Scientific journals in Japanese. The original audience of this web lecture was the new graduate students in our group. This is now being made open to public in the hope that it might be helpful to the students of theoretical physics in general, and also to graduate students elsewhere who are interested in the subject after seeing the the related subject discussed in reaserach journals and web pages. The last but not the least inteded audience is the active reserachers of fundamental aspects of quantum mechanics who are in search of more accessible matrials for our publications in reaserach journals.
Quantum Graph theory, aka. quantum theory of points and lines, is quantum mechanics applicable to the quantum device which is at the core of comming quantum technology. In its deceptive elementary guise, it houses such exotica as renormalization, quantum anomaly, aholonomy which usualy are found only in the realm of ultra high energy physics.
Pedagogically, it could be regared as a precious subject in which advanced modern aspects of quantum physics can be leart in very elementary settings. It is just like a Prague Mariotte Theatre rendition of that incomparable opera Don Giovanni. With proper production under able director, the artistic essence of this devine comedy can be recreated within the limited space of puppets.
The material found in this lecture is basically the results of the original research of this author and collaborators. My intension is to provide one-stop review in accessible language for a subject which are scattered in some ten original research papers. Readers should feel free to quote it with appropriate reference to this website for research and educational purposes. Other reuse, commercial, political, defamatory etc. are strongly discouraged.
I would like to express my gratitude to my co-researchers, Dr. Takaomi Shigehara, Dr. Izumi Tsutsui and Dr. Tamas Fulop. Without their contributions, there wouldn't have been any materials found here ever developed. Needless to say, possible errors found here, on the other hand, are of course the sole responsibility of tjis author.
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