Theory and Applications of the Poincaré Group

本書主要作為一個教學工具，旨在幫助那些希望深入理解群論的人，透過適用於物理世界的例子，或是從群論的角度理解物理世界的對稱性特徵。無論是高級學生還是對群論與物理學之間關係感興趣的學者，都會發現本書具有啟發性。特別是從事高能物理學和量子力學基礎研究的人，將會發現本書在相對論量子力學的例子上非常豐富。

這一新版包含四個新章節，其中兩個章節與狄拉克的目標一致，旨在結合二十世紀物理學的重要發展，即量子力學和特殊相對論。此外，這些新章節還討論了現在被理解為相互關聯的各種經典和量子光學方面。大多數原始章節已進行更新，無論是新增材料或在某些情況下對原始內容的重新詮釋。章節的順序已重新安排，以創造更具凝聚力的呈現方式。第一版的原始目的，即提供物理學學生和研究人員可以關聯的例子，並未改變。

Young S. Kim came to the United States from South Korea in 1954 after high school graduation to become a freshman at the Carnegie Institute of Technology (now called Carnegie Mellon University) in Pittsburgh. In 1958, he went to Princeton University for graduate study in physics and received his PhD degree in 1961. In 1962, he became an assistant professor at the University of Maryland at College Park near Washington, DC. After going through the academic ranks of associate and full professors, Dr. Kim became a professor emeritus in 2007. This is still his position at the University of Maryland.

Dr. Kim's thesis advisor at Princeton was Sam Treiman, but he had to go to Eugene Wigner whenever he had to face fundamental problems in physics. During this process, he became interested in Wigner's 1939 paper on internal space-time symmetries particles in Einstein's Lorentz-covariant world. Since 1973, his publications have been based primarily on constructing mathematical formulae for understanding Wigner's paper. In 1988, Dr. Kim noted that the same set of mathematical devices are applicable to squeezed states in quantum optics. Since then, he has been publishing papers also on optical and information sciences. These days, Dr. Kim publishes articles on the question of whether quantum mechanics and special relativity can be derived from the same basket of equations.

Sibel Başkal is Professor Emerita of Physics at the Middle East Technical University. She is particularly interested in the manifestations of the Poincaré and little groups, and of group contractions in physical sciences. Her research interests extend to current problems in classical field theories, mostly on alternative approaches to Einstein's gravity. She has published more than 30 peer-reviewed papers and is the co-author of three books with Y.S.Kim and M.E.Noz.

Marilyn E. Noz is Professor Emerita in the Department of Radiology at NYU School of Medicine. Over the last more than 40 years, she has collaborated with Professor Kim on relativistic quantum mechanics using two-by-two matrices, harmonics oscillators, and the Lorentz group. She has contributed to over 50 peer-reviewed journal articles in elementary particle physics and optics. She has written three books with Professor Kim and three books with Professors Kim and Başkal. She continues to do research in elementary particle physics and quantum optics. Professor Noz taught physics at Marymount College, Tarrytown, NY for five years, where she instituted a major in Physics. She then went to Indiana University of Pennsylvania where she taught physics for five years, rotating through most of the graduate and undergraduate courses. In 1974 she went to the New York University School of Medicine where she taught physics to radiology residents and students training to be ultrasound or nuclear medicine technologists. She has about one hundred refereed journal articles in medical related journals, where she used her physics background. Together with her co-author, Professor Gerald Q. Maguire Jr, she has published four books concerning radiation protection in the radiologic and health sciences.

Young S. Kim於1954年從南韓來到美國，畢業於高中後成為卡內基技術學院（現稱卡內基梅隆大學）的一年級新生，該校位於匹茲堡。1958年，他前往普林斯頓大學攻讀物理研究生學位，並於1961年獲得博士學位。1962年，他成為馬里蘭大學（University of Maryland）哥倫比亞公園校區的助理教授，該校靠近華盛頓特區。經歷了副教授和正教授的學術晉升後，金博士於2007年成為名譽教授。這仍然是他在馬里蘭大學的職位。

金博士在普林斯頓的論文指導教授是Sam Treiman，但每當面對物理學中的基本問題時，他都必須去找Eugene Wigner。在這個過程中，他對Wigner在1939年發表的有關愛因斯坦洛倫茨協變世界中粒子的內部時空對稱性的論文產生了興趣。自1973年以來，他的出版物主要基於構建數學公式以理解Wigner的論文。1988年，金博士注意到同一組數學工具也適用於量子光學中的擠壓態。自那時以來，他也開始發表有關光學和信息科學的論文。如今，金博士發表的文章探討量子力學和特殊相對論是否可以從同一組方程式推導出來。

Sibel Bașkal是中東技術大學的物理名譽教授。她特別對Poincaré和小群體的表現以及物理科學中的群體收縮感興趣。她的研究興趣擴展到當前的經典場論問題，主要集中在愛因斯坦重力的替代方法上。她已發表超過30篇經過同行評審的論文，並與Y.S. Kim和M.E. Noz共同撰寫了三本書。

Marilyn E. Noz是紐約大學醫學院放射科的名譽教授。在過去的40多年中，她與金教授合作研究使用二乘二矩陣、諧波振盪器和洛倫茨群的相對論量子力學。她在基本粒子物理學和光學方面貢獻了超過50篇經過同行評審的期刊文章。她與金教授共同撰寫了三本書，並與金教授和Bașkal教授共同撰寫了三本書。她繼續在基本粒子物理學和量子光學領域進行研究。Noz教授在紐約塔里敦的Marymount College教授物理學五年，並設立了物理學專業。隨後，她前往賓夕法尼亞州的印第安納大學教授物理學五年，涵蓋了大多數研究生和本科課程。1974年，她前往紐約大學醫學院，教授放射科住院醫師和接受超聲或核醫學技術訓練的學生物理學。她在醫學相關期刊上發表了約一百篇經過審核的期刊文章，並利用她的物理背景。與她的合著者Gerald Q. Maguire Jr教授一起，她出版了四本有關放射線防護的書籍，涉及放射學和健康科學。