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Physics - Theoretical, Mathematical & Computational Physics | From Classical to Quantum Fields - An Introduction to the Path Integral Formalism

From Classical to Quantum Fields

An Introduction to the Path Integral Formalism

Seneor, Roland, Baulieu, Laurent, Iliopoulos, Jean

2016, Approx. 300 p. 5 illus.

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  • About this textbook

  • The book is an advanced text which grew from courses taught at the famous Ecole Polytechnique
  • Provides a modern approach to field theory, with exercises, questions and hints to assist in understanding the content
  • More technically advanced than competing titles, especially in the uses of mathematics as a tool

Quantum field theory has enormously matured during the last two decades.  It provides an extremely powerful tool to describe a large variety of fundamental physical phenomenoa over many scales of distances.  Once a specialized field in elementary particle physics, quantum field theory has since been dramatically extended to cover many areas from condensed matter physics to quantum gravity and even new developments in mathematics.

This evolution has implied a corresponding evolution in University curricula.  Quantum field theory is no longer limited to specialized graduate schools, but it is considered an essential subject in general physics education.

From Classical to Quantum Fields grew out of courses taught by the authors during the last decade to students in Ecole Polytechnique and Ecole Normale Superieure in Paris.  One of the purposes of the course was to show them how mathematics and physics are intimately connected and how they enrich each other:  how physics lies at the origin of many concepts introduced in mathematics and how mathematics is far more than a convenient language for physics.

The passage from the intuitive picture of classical fields to that of quantum field theory, through the notion of path integral quantization, provides an ideal framework.  Emphasis is given to a clear exposition of the underlying principles.

The basic elements about path integrals are gradually introduced, starting from quantum mechanics and finishing with the modern techniques for defining and renormalizing Yang-Mills theories.  The power of this approach has overshadowed the more traditional quanization schemes, first because most physically interesting systems have a gauge invariance and second because it provides for any system the most efficient way to perform numerical non-perturbative calculations.  The relation between renormalization and symmetries is analyzed in examples with the introduction of the notion of anomalies.

Some new ideas concerning supersymmetry and topological symmetries are also introduced without much development.  The last chapter, "Beyond the Standard Model," will motivate readers to pursue further studies of quantum field theory.

Content Level » Research

Keywords » path integral - quantum mechanics - quantum theory - symmetries

Related subjects » Classical Continuum Physics - Quantum Physics - Theoretical, Mathematical & Computational Physics

Table of contents 

Relativistic Invariance.- The Electromagnetic Field.- Physical States.- The Dirac Equation.

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