Particle-Field Duality and Form Factors from Vertex Operators

Abstract

Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values of such vertex operators in the space of fields. The vertex operators can be constructed explicitly in radial quantization. Furthermore, these vertex operators can be exactly bosonized in momentum space. We develop these ideas by studying the free-fermion point of the sine-Gordon theory, and use this scheme to compute some form-factors of some non-free fields in the sine-Gordon theory. This work further clarifies earlier work of one of the authors, and extends it to include the periodic sector.

17 pages, 2 figures, CLNS 93/???

References in corpus (5)

• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Free Field Representation For Massive Integrable Models
• Correlators of the Jost functions in the Sine-Gordon model
• Free Field Representation for the Classical Limit of Quantum Affine Algebra
• Spectrum Generating Affine Lie Algebras in Massive Field Theory

Cited by in corpus (8)

• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap
• Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement
• Form Factors, Thermal States and Modular Structures
• Correlation functions of twist fields from Ward identities in the massive Dirac theory
• Topological Correlation Functions in Minkowski Spacetime
• More General Correlation Functions of Twist Fields From Ward Identities in the Massive Dirac Theory
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory