Construction of two-dimensional quantum electrodynamics

Journal Article · Sun Jun 01 04:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524587· OSTI ID:5361425

Ito, K R

We investigate quantum electrodynamics in two dimensions, (QED)/sub 2/, in the constructive method. We construct a cutoff Hamiltonian defined on the Fock space with an indefinite metric, and discuss its properties and renormalization counterterms. When the fermion is massless, this model is exactly solvable (known as the Schwinger model). We study the massless model through the Bogolyubov transformation (canonical linear transformation) extended to this Fock space, through which the properties of the Hamiltonian and the physical vacuum are clarified. When the mass of the fermion Mnot =0, we discuss the transformation of the renormalized Hamiltonian into the one of the so-called sine-Gordon model. The properties of the operator which implements this transformation are clarified; it is an unbounded operator which is isometric with respect to the indefinite metric.

• Research Organization: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, Japan
• OSTI ID: 5361425
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOGOLYUBOV TRANSFORMATION
CANONICAL TRANSFORMATIONS
ELECTRODYNAMICS
FERMIONS
FIELD THEORIES
FOCK REPRESENTATION
HAMILTONIANS
MASS RENORMALIZATION
MATHEMATICAL OPERATORS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
SCHWINGER SOURCE THEORY
TWO-DIMENSIONAL CALCULATIONS
VECTOR FIELDS