Towards quantum noncommutativeκ-deformed field theory

Quantum Field Theory on the q–deformed Fuzzy Sphere

We discuss the second quantization of scalar field theory on the q–deformed fuzzy sphere S2 q,N for q ∈ IR, using a path–integral approach. We find quantum field theories which are manifestly covariant under Uq(su(2)), have a smooth limit q → 1, and satisfy positivity and twisted bosonic symmetry properties. Using a Drinfeld twist, they are equivalent to ordinary but slightly “nonlocal” QFT’s o...

Towards chaos criterion in quantum field theory

Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations. Phenomenon of chaos attracts much attention in various fields of physics. Originally it was associated with...

Towards an Ontology for Quantum Field Theory

The recent work of P. Teller and S. Auyang in the philosophy of Quantum Field Theory (QFT) has stimulated the search for the fundamental entities of that theory. In QFT, the classical notion of a particle collapses. The theory does not only forbid classical, i.e. spatiotemporally identifiable particles, but it makes particles of the same type conceptually indistinguishable. Teller and Auyang ha...

A brief overview of quantum field theory with deformed symmetries and their relation with quantum gravity

The Master Field for QCD and q-Deformed Quantum Field Theory

The master fields for the large N limit of matrix models and gauge theory are constructed. The master fields satisfy to standard equations of relativistic field theory but fields are quantized according to a new rule. To define the master field we use the Yang-Feldman equation with a free field quantized in the Boltzmannian Fock space. The master field for gauge theory does not take values in a...