John R Klauder - Böcker

This text describes novel treatments of quantum problems using enhanced quantization procedures. When treated conventionally, certain systems yield trivial and unacceptable results. This book describes enhanced procedures, generally involving extended correspondence rules for the association of a classical and a quantum theory, which, when applied to such systems, yield nontrivial and acceptable results. The text begins with a review of classical mechanics, Hilbert space, quantum mechanics, and scalar quantum field theory. Next, analytical skills are further developed, a special class of models is studied, and a discussion of continuous and discontinuous perturbations is presented. Later chapters cover two further classes of models both of which entail discontinuous perturbations. The final chapter offers a brief summary, concluding with a conjecture regarding interacting covariant scalar quantum field theories. Symmetry is repeatedly used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included.

This text describes novel treatments of quantum problems using enhanced quantization procedures. When treated conventionally, certain systems yield trivial and unacceptable results. This book describes enhanced procedures, generally involving extended correspondence rules for the association of a classical and a quantum theory, which, when applied to such systems, yield nontrivial and acceptable results. The text begins with a review of classical mechanics, Hilbert space, quantum mechanics, and scalar quantum field theory. Next, analytical skills are further developed, a special class of models is studied, and a discussion of continuous and discontinuous perturbations is presented. Later chapters cover two further classes of models both of which entail discontinuous perturbations. The final chapter offers a brief summary, concluding with a conjecture regarding interacting covariant scalar quantum field theories. Symmetry is repeatedly used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included.

This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstratively improved procedures.

Alladi Ramakrishnan (1923–2008) was an eminent scientist who had a wide range of research interests in theoretical and mathematical physics. Professor Ramakrishnan made signi?cant contributions to probability and statistics, elem- tary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Ramakrishnan believedstrongly that in addition to doing fun- mental research, one must contribute to the advancementof the profession. Inspired by his visit to the Institute for Advanced Study in Princeton in 1957–1958, he returned to Madras and began the Theoretical Physics Seminar at his family home Ekamra Nivas. These seminars were ultimately responsible for the creation of MATSCIENCE, The Institute of Mathematical Sciences in 1962. This institute, of which he was the Director for its ?rst 21years, has grown steadily in size and stature, and is his monumental contribution to the profession. In a distinguished scienti?c life that has spanned more than ?ve decades, Professor Ramakrishnan has come into close contact with, and was in?uenced by, several eminent mathema- cians and physicists, and has moulded the careers of his several students and young researchers. This volume, which is a tribute to his great legacy, not only deals with his signi?cant contributions to research and the profession, but also contains a ?ne collection of research and survey papers by leading physicists and mathematicians that cover a broad range of areas in the mathematical sciences.

Alladi Ramakrishnan (1923–2008) was an eminent scientist who had a wide range of research interests in theoretical and mathematical physics. Professor Ramakrishnan made signi?cant contributions to probability and statistics, elem- tary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Ramakrishnan believedstrongly that in addition to doing fun- mental research, one must contribute to the advancementof the profession. Inspired by his visit to the Institute for Advanced Study in Princeton in 1957–1958, he returned to Madras and began the Theoretical Physics Seminar at his family home Ekamra Nivas. These seminars were ultimately responsible for the creation of MATSCIENCE, The Institute of Mathematical Sciences in 1962. This institute, of which he was the Director for its ?rst 21years, has grown steadily in size and stature, and is his monumental contribution to the profession. In a distinguished scienti?c life that has spanned more than ?ve decades, Professor Ramakrishnan has come into close contact with, and was in?uenced by, several eminent mathema- cians and physicists, and has moulded the careers of his several students and young researchers. This volume, which is a tribute to his great legacy, not only deals with his signi?cant contributions to research and the profession, but also contains a ?ne collection of research and survey papers by leading physicists and mathematicians that cover a broad range of areas in the mathematical sciences.

The book consists of lectures delivered at the International Symposium on Coherent States: Past, Present, and Future, held in Oak Ridge, Tennessee, June 14 - 17 1993. Both theoretical and experimental subjects are treated. Theoretical subjects dealt with include quantum optics, quantum chaos, condensed matter physics, nuclear physics, high energy physics and foundational issues such as quantum-classical connections and various semiclassical quantization schemes. Experimental topics dealt with principally concern atomic and molecular physics and especially lasers. Topics related to coherent states, most notably wavelets, are also included.

The book consists of lectures delivered at the International Symposium on Coherent States: Past, Present, and Future, held in Oak Ridge, Tennessee, June 14 - 17 1993. Both theoretical and experimental subjects are treated. Theoretical subjects dealt with include quantum optics, quantum chaos, condensed matter physics, nuclear physics, high energy physics and foundational issues such as quantum-classical connections and various semiclassical quantization schemes. Experimental topics dealt with principally concern atomic and molecular physics and especially lasers. Topics related to coherent states, most notably wavelets, are also included.

This pioneering book addresses the question: Are the standard procedures of canonical quantization fully satisfactory, or is there more to learn about assigning a proper quantum system to a given classical system? As shown in this book, the answer to this question is: The standard procedures of canonical quantization are not the whole story!This book offers alternative quantization procedures that complete the story of quantization. The initial chapters are designed to present the new procedures in a clear and simple manner for general readers. As is necessary, systems that exhibit acceptable results with conventional quantization lead to the same results when the new procedures are used for them. However, later chapters examine selected models that lead to unacceptable results when quantized conventionally. Fortunately, these same models lead to acceptable results when the new quantization procedures are used.

This volume is a review on coherent states and some of their applications. The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics. Particular emphasis is given to a general historical introduction, general continuous representations, generalized coherent states, classical and quantum correspondence, path integrals and canonical formalism. Applications are considered in quantum mechanics, optics, quantum chemistry, atomic physics, statistical physics, nuclear physics, particle physics and cosmology. A selection of original papers is reprinted.