Non-Linear Field Theories II. Canonical Equations and Quantization

Canonical quantization of non-local field equations

We consistently quantize a class of relativistic non-local field equations characterized by a non-local kinetic term in the lagrangian. We solve the classical non-local equations of motion for a scalar field and evaluate the on-shell hamiltonian. The quantization is realized by imposing Heisenberg’s equation which leads to the commutator algebra obeyed by the Fourier components of the field. We...

Quantization of Non-Polynomial Field Theories

Quantization of Non-polynomial Field Theories

We reexamine the quantization of a class of non-polynomial scalar field theories which interpolates continuously from a free one to φ 4 theory. The quantization of such theories is problematic because the Feynman rules may not be directly obtained. We give a means for calculating the correlation functions in this theory. The Feynman rules developed here shall enable further progress in the unde...

Canonical quantization, twistors and relativistic wave equations

A formulation of relativistic quantum mechanics in twistor space is studied. The phase-space description of the classical theory leads (via canonical quantization) to all known wave equations describing massless particles. A natural link between the classical and the quantum description is provided by the Wigner function de®ned on the space of twistors.

Canonical Quantization of Noncommutative Field Theory

A simple method to canonically quantize noncommutative field theories is proposed. As a result, the elementary excitations of a (2n + 1)-dimensional scalar field theory are shown to be bilocal objects living in an (n + 1)-dimensional space-time. Feynman rules for their scattering are derived canonically. They agree, upon suitable redefinitions, with the rules obtained via star-product methods. ...