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01/09/01 Colloquium
DR. COSTAS EFTHIMIOU
DEPARTMENT OF PHYSICS
UNIVERSITY OF CENTRAL FLORIDA
DEPARTMENT OF PHYSICS
UNIVERSITY OF CENTRAL FLORIDA
Quantum Field Theory: The Interface Between Math and Physics; A Guide For Mathematicians
Abstract: This talk will attempt to explain at an elementary level, the relation between the Yang-Mills (or Gauge) theories in physics and the mathematical framework of fiber bundles. In particular, it will focus on the following questions: What is a gauge field? How does it relate to a force? What are the fiber bundles? How do they appear in physics? What does it mean for a fiber bundle to have a connection? How are the concepts of a connection and a gauge field related? Having discussed the answers to these questions, the Millennium Prize Problem for the Yang-Mills theories will be stated in a rigorous mathematical language. [The solution of the Millennium Prize Problem will be left as a HW exercise for the audience!]