Mark S Swanson

Path Integral Quantization (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book is an essential introduction to the techniques and applications of path integral quantization and functional techniques. Its intended audience is both students and practitioners who desire a basic and concise introductory overview of path integral and functional methods. The first half of the text focusses on quantum mechanics. It begins with a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, along with relevant mathematics. The path integral representation of quantum mechanically important mathematical quantities is then derived from standard quantum mechanics for a variety of physical systems employing both bosonic and Grassmann variables, demonstrating the relationship of the path integral to standard quantum mechanics and operator methods. The path integral is then evaluated by a variety of techniques for quantum mechanical transition amplitudes and fixed energy wave functions and tunnelling. The book derives the WKB approximation and the role of classical solutions to the equation of motion. It evaluates the partition function, the application of canonical transformations, and transition elements in the presence of constraints. The second half of the text focusses on relativistic field theories. After reviewing special relativity, the book derives the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. In particular, the text analyses the role of constraints in gauge field theory. The path integral functional method for perturbation theory is developed. Symmetry relations as well as the quantization of nonabelian gauge theories are presented using path integral methods. Nonperturbative methods for lower dimensional Yang-Mills theory are presented, as well as deriving the Dirac quantization condition and the role of classical solutions to the equations of motion in the field theory path integral.

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Produktdetails

• Verlag: Institute of Physics Publishing
• Seitenzahl: 230
• Erscheinungstermin: 6. August 2020
• Englisch
• ISBN-13: 9780750335478
• Artikelnr.: 59949650

Autorenporträt

Mark Swanson received his PhD in physics from the University of Missouri at Columbia in 1976 under the supervision of Justin Huang. After postdoctoral appointments at the University of Alberta and the University of Connecticut he held a faculty appointment at the University of Connecticut at Stamford from 1983 to 2014, during which time he spent six years in university administrative roles. He is the author of 25 research articles and three other monographs with an emphasis on field theory and path integral techniques. He is currently an emeritus professor of physics at the University of Connecticut.