Field Theory on a q = −1 Quantum Plane

ar X iv : q - a lg / 9 50 30 07 v 1 1 6 M ar 1 99 5 Field Theory on q = − 1 Quantum Plane

We build the q = −1 defomation of plane on a product of two copies of algebras of functions on the plane. This algebra constains a subalgebra of functions on the plane. We present general scheme (which could be used as well to construct quaternion from pairs of complex numbers) and we use it to derive differential structures, metric and discuss sample field theoretical models. TPJU 4/95 Februar...

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...

A Quantum field theory of dyons 1

We construct a classical field theory action which upon quantization via the functional integral approach, gives rise to a consistent Dirac–string independent quantum field theory. The approach entails a systematic derivation of the correlators of all gauge invariant observables, and also of charged dyonic fields. Manifest SO(2)– duality invariance and Lorentz invariance are ensured by the PST–...

Quantum Theory on a Galois Field

Systems of free particles in a quantum theory based on a Galois field (GFQT) are discussed in detail. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily describes a particle and its antiparticle simultaneously. As a consequence, well known results of the standard theory (spin-statistic...

Lectures on quantum field theory