Related papers: Field Theory on $q=-1$ Quantum Plane
In this work, we construct the de Rham complex with differential operator d satisfying the Q-Leibniz rule, where Q is a complex number, and the condition $d^3=0$ on an associative unital algebra with quadratic relations. Therefore we…
I report on work on a Lagrangian formulation for the simplest 1+1 dimensional integrable hierarchies. This formulation makes the relationship between conformal field theories and (quantized) 1+1 dimensional integrable hierarchies very…
A Cartan Calculus of Lie derivatives, differential forms, and inner derivations, based on an undeformed Cartan identity, is constructed. We attempt a classification of various types of quantum Lie algebras and present a fairly general…
We study the quantum invariants of projective varieties over the number fields. Namely, explicit formulas for a functor $\mathscr{Q}$ on such varieties are proved. The case of abelian varieties with complex multiplication is treated in…
We build a four-dimensional quaternion-parametrized conformal field theory (QCFT) using quaternion holomorphic functions as the generators of quaternionic conformal transformations. Taking the two-dimensional complex-parametrized conformal…
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…
We give a broad overview of a construction of a theory for matter on fixed causal set backgrounds. We introduce the Sorkin-Johnston formalism for a free (real) scalar field theory that is applicable to regions of continuum spacetimes as…
We obtain a condensed reconstruction of algebraic quantum theory, emphasizing its foundational aspects and algebraic structure. We obtain the $W^*$-algebra structure from elementary assumptions about observers and how they can observe…
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
We present a method for tabulating all cubic function fields over $\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up to a given bound…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We construct a family of irreducible representations of the quantum plane and of the quantum Weyl algebra over an arbitrary field, assuming the deformation parameter is not a root of unity. We determine when two representations in this…
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the…
We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space ${\bf R}_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary ${\bf R}^N$.…
A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how…
The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of…
I introduce a reality structure on the Heisenberg double of Fun_q(SL(N,C)) for q phase, which for N=2 can be interpreted as the quantum phase space of the particle on the q-deformed mass-hyperboloid. This construction is closely related to…
We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…