Quantum Theory of Generalized Gauge Field

Quantum Gauge Field Theory in Cohesive Homotopy Type Theory

The observable world of physical phenomena is fundamentally governed by quantum gauge field theory (QFT) [16], as was recently once more confirmed by the detection [13] of the Higgs boson [8]. On the other hand, the world of mathematical concepts is fundamentally governed by formal logic, as elaborated in a foundational system such as axiomatic set theory or type theory. Quantum gauge field the...

Gauge invariance in wavelet - based quantum field theory

Continuous wavelet transform has been attracting attention as a possible tool for regulari-sation of gauge theories since the first paper of Feredbush [1]. However, up to the present time, this tool has been used only for identical substitution of the local fields in the local action S[φ(x)] : φ(x) → φ(x) = 1 C ψ 1 a d ψ x − b a φ a (b) dad d b a , where φ a (b) is a field measured at point b w...

Gauge Fixing and Renormalization in Topological Quantum Field Theory*

In this letter we show how Witten’s topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero. Submitted to Phys. Lett. * Work supported by the Departme...

An axiomatic approach to Quantum Gauge Field Theory

In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connectio...

Gauge Field Theory Models