Operator Equations in Two Field Theory Models

On momentum operator in quantum field theory

The interrelations between the two definitions of momentum operator, via the canonical energy-momentum tensorial operator and as translation operator (on the operator space), are studied in quantum field theory. These definitions give rise to similar but, generally, different momentum operators, each of them having its own place in the theory. Some speculations on the relations between quantum ...

The Theory of Singular Differential-Operator Equations

We consider methods of reduction of differential operator equations with the Fredholm operator in the main expression to regular problems. Relation between the initial conditions choice problem and the Jordan structure of operator coefficients of equations is shown. The theorem of existence and uniqueness of the initial problem is proved. The method of fundamental operators is used for construc...

Lattice Versions of Quantum Field Theory Models in Two Dimensions

Algebraic Quantum Field Theory and Operator Algebras

In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as " why mathematicians are/should be interested in algebraic quantum field theory " would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may s...

A Field Theory for the Read Operator

We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Read’s original work we do not work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our ...