Field Theory: A Path Integral Approach
This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas. Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.
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Preface to the Second Edition
Path Integrals and Quantum Mechanics
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aFaF anti-commutation assume bosonic boundary conditions calculate chiral transformation classical field commutation Consequently constant coordinate correspond cosh d2xE defined denotes derivative determinant diagram dynamical eigenstates eigenvalues ensemble Euclidean Euler-Lagrange equation evaluate exponent fact fermionic fermionic oscillator Feynman field variables function in Eq Furthermore gauge field gauge fixing gauge invariance gauge theories gauge transformation ghost given Grassmann variables Green's function Hamiltonian harmonic oscillator infinitesimal instanton integrand Ising model Lagrangian density lattice Let us consider Let us note Let us recall magnetization matrix elements Maxwell's theory momentum namely note from Eq obtain operator parameter of transformation particle partition function path integral Phys physical potential propagator quadratic quantization quantum field theory quantum mechanical system relation in Eq satisfy scalar field Schrodinger equation solution space-time spin superpotential supersymmetric symmetry takes the form temperature term tion trajectory transition amplitude vacuum vanishes wave function write