Related papers: Unitarity in the noncommutative theories

The no-communication theorem states that the observation of a subsystem of an entangled state does not affect another subsystem. Nevertheless, this theorem is based on the assumption that all quantum processes are unitary. We examine a…

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…

Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector…

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…

We answer a question of Pakhomov by showing that there is a consistent, c.e. theory $T$ such that no theory which is definitionally equivalent to $T$ has a computable model. A key tool in our proof is the model-theoretic notion of mutual…

The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.

In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…

We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.

We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.

In the present paper we give conclusive arguments pointing at physical equivalence among conformally related metrics. Based on the argument that any consistent effective theory of spacetime must be invariant under the one-parameter group of…

We prove that the isoperimetric constant is positive for all symmetric spaces of noncompact type and compute it explicitly.

We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras…

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

After an overview of noncommutative differential calculus, we construct parts of it explicitly and explain why this construction agrees with a fuller version obtained from the theory of operads.

We argue that quantum theory in curved spacetime should be invariant under the continuous spacetime symmetries thaat are connected with the identity. For typical warped-product spacetimes, we prove that such invariance can be actually…

The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum…