A Pedestrian Approach to Quantum Field Theory

Edward G Harris

• Editorial: Dover Publications
• Año: 2014
• ISBN:
  9780486793290
• Categoría: Sciences physiques
• Categoría: Théorie des quanta

Written by a renowned professor of physics, this introductory text is geared toward graduate students taking a year-long course in quantum mechanics in which the third quarter is devoted to relativistic wave equations and field theory. Difficult concepts are introduced gradually, and the theory is applied to physically interesting problems.
After an introductory chapter on the formation of quantum mechanics, the treatment advances to examinations of the quantum theory of the free electromagnetic field, the interaction of radiation and matter, second quantization, the interaction of quantized fields, and quantum electrodynamics. Additional topics include the theory of beta decay, particles that interact among themselves, quasi particles in plasmas and metals, and the problem of infinities in quantum electrodynamics. The Appendix contains selected answers to problems that appear throughout the text.

1

The Formalism of Quantum Mechanics

It is not an easy task to state the “rules” of quantum mechanics. Many textbooks do not even try and yet succeed in conveying to the reader a working knowledge of the subject. In this book the rules of quantum mechanics and some elementary results are collected in one place for ease of reference. In the sections that follow we give a brief account of the foundations of quantum mechanics. A more detailed discussion of the subject can be found in von Neumann⁵ and in the more recent book by Jauch.⁶ We begin by discussing the mathematical structure known as a Hilbert space and then give the rules for describing the real world in terms of this mathematical structure.

HILBERT SPACE

A Hilbert space

is an abstract set of elements called vectors

,

, and so on, having the following set of properties:

1. The space

is a linear vector space over the field of complex numbers such as λ, and μ. It has three properties. (a) For each pair of vectors there is determined a vector called the sum such that

(b) One vector

is called the ...