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The essential role of functional integrals in modern physics

Chapter 3 illustrates by a number of examples the essential role of functional integrals in physics. For example, the path integral representation of quantum mechanics explains why many basic equations of classical physics satisfy a variational principle, the relation between quantum field theory and the theory of critical phenomena in macroscopic phase transitions. Field integrals are essential for gauge theory quantization, leading to the introduction of Faddeev–Popov ghost fields and BRST symmetry. Lattice gauge theory, the discretized form of field integrals, makes non–perturbative calculations possible. These are at the basis of the calculation of penetration effects in quantum field theory (instanton calculus).