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Delaware State University Department of Applied Mathematics and Theoretical Physics Dover, DE 19901 Introduction to Field Theory 60-741-00, 3 cr. Text: K. Huang: Quantum Field Theory: From Operators to Path Integrals recommended: A. Zee: Quantum Field Theory in a Nutshell M. Peskin, D.V. Schroeder: An introduction to Quantum Field Theory The aim of the course is to introduce, develop and discuss various methods of nonrelativistic and relativistic field theory. Students are strongly encouraged to study particular topics mentioned in the course, in detail and depth surpassing the discussions in class, as well as the last three chapters, not covered in class: The Gaussian fixed point, In two dimensions, Topological excitations. This then is the purpose of the term paper. Prerequisite: Mathematical methods of Physics IV (26-667) or equivalent (vector calculus, linear algebra, tensors, real and complex analysis, multivariate calculus), Classical Mechanics (26-652), Advanced Electromagnetic Theory II (26-672). A successful student is expected to gain a working knowledge of the covered material, so as to be able to (1) follow the applications in the literature, (2) solve typical problems in the field, and (3) discuss adequately the term-paper subject. Topical schedule: Introducing Quantum Fields, Scalar Fields Relativistic Fields, Canonical Formalism Electromagnetic Field Dirac Equation & Dirac Field Dynamics of Interacting Fields Feynman Graphs Vacuum Correlation Functions Quantum Electrodynamics and Its Processes Perturbative Renormalization Path Integrals Broken Symmetry Renormalization 1. Course Title/Number: Introduction to Field Theory / 60-741-00 2. Number of Credits: 3 CURRICULUM COURSE REVIEW: Introduction of Field Theory 3. Curriculum Program Title: Ph.D. in Applied Mathematics and Theoretical Physics 4. Curriculum/Course is: [X] New [ [ Required Course [X] ] ] Revised Elective Course 5. List Prerequisites: 26-667 (Mathematical methods of Physics IV), or equivalent (vector calculus, linear algebra, tensors, real and complex analysis, multivariate calculus) 26-652 (Classical Mechanics) 26-672 (Advanced Electromagnetic Theory II) 6. List Courses Being Replaced or Changed: This is a new course. 7. List Courses Being Deleted: No courses are being deleted. 8. Needs Statement: This course is needed for students pursuing a Ph.D. with concentration in theoretical physics and especially for those interested in fundamental physics, where field theory provides one of the main overarching concepts in the contemporary understanding of the real world. 9. Catalog Description of the Course: This course introduces, develops and discusses various methods and techniques of continuous (quantum) field theory, foremost as developed for particle physics, but with numerous applications in other fields including condensed matter physics. 10. List of Objectives of the Course: (1) To provide an introduction to the body knowledge and techniques of quantum field theory. (2) To see how these techniques apply to the analysis of the various phenomena from electromagnetism to the unified field theory. (3) To learn how to identify those phenomena throughout theoretical physics, which are best described using these methods. (4) To develop the problem-solving skills associated with the application of these methods in theoretical physics, and learn how to extract experimentally verifiable information from such application. CURRICULUM COURSE REVIEW: Superstrings and Beyond 11. Course Outline: See the “Topical schedule” section in the attached brief syllabus. 12. Show how the proposed course fits into the curriculum or course sequence: This course is an elective within the curriculum of the Ph.D. program in theoretical physics, and is indispensable for students focusing on fundamental physics. For an overview of pre-requisite dependences and the course’s relation to other courses proposed herein, please see the attached “Proposed Course Dependencies” chart. 13. Are there comparable courses in other departments? No. 14. How will the students be affected by this course change? This course provides the students an opportunity to increase their integration with the research program of the Department of Applied Mathematics and Theoretical Physics, by understanding the mathematical underpinnings of the techniques that are used in contemporary theoretical physics. This course will improve students’ professional competence, employability in technical fields and ability to pass professional examinations; the term paper requirement will foster improving expository skills. Neither this course nor its prerequisites increase the total number of semester hours in this curriculum or the number of credit hours required for graduation. 15. What effect will this new course have on College resource? None: this course will not require new or additional resources or staffing. 16. How will the course benefit the College? This course studies the interactive dynamics continuous fields, which is one of the unifying themes in the contemporary understanding of all fundamental physics. Besides this ubiquity of its key ideas, field theory also provides the example of the most accurate agreement between theory and experiment in all history of science, which may then also serve as a case study, interesting to students of the philosophy and sociology of science. 17. How will the change affect the program? This course will introduce students to the study of continuous fields, their propagation and interactions. As a generalization of the theories of electromagnetic and gravitational fields, this course provides an introduction to one of the unifying themes in the overall philosophy and methodology of CURRICULUM COURSE REVIEW: Introduction of Field Theory contemporary theoretical physics, and so is pivotal in the curriculum of any theoretical physicist. This course will be one of the electives specific to the Ph.D. program (concentration in theoretical physics) in this department. 18. Evaluation of Student Performance: Homework Assignments 40 % Term-paper (take-home final) 60 % Sample homework assignments, in-term and final examination question-sheets, work sheets, course notes, review sheets and term papers will be accessible on-line. Course Structure: Three (3) 50-minute lectures per week. References 1. K. Huang: Quantum Field Theory: From Operators to Path Integrals (Springer-Verlag, 2004, ISBN = 0387983848) 2. A. Zee: Quantum Field Theory in a Nutshell (Dover Publications, 1992; ISBN = 0486670473) 3. M. Peskin, D.V. Schroeder: An introduction to Quantum Field Theory (Oxford University Press, 2004; ISBN = 0198566336) Submitted to Department of Applied Mathematics and Theoretical Physics by: Tristan Hubsch, on 27th of November, 2007.