Related papers: Inequivalent Vacuum States in Algebraic Quantum Th…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
In quantum gravity, one looks for alternative structures to spacetime physics than ordinary real manifolds. Here, we propose an alternative universal construction containing the latter as an equilibrium state under the action of the…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
We investigate the interaction of the gravitational field with a quantum particle. First, we give the proof of the equality of the inertial and the gravitational mass for the nonrelativistic quantum particle, independently of the…
The existence of inequivalent representations in quantum field theory with {\it finitely} many degrees of freedom is shown. Their properties are exemplified and analysed for concrete and simple models. In particular the relations to…
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
Within the recently proposed structure-inclusive algebraic formulation of quantum field theory, we show that a massless particle can acquire mass by special nonlinear coupling to a universal massless scalar field; establishing an…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
The early universe provides an opportunity for quantum gravity to connect to observation by explaining the large-scale structure of the Universe. In the group field theory (GFT) approach, a macroscopic universe is described as a GFT…
Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
It is known that the quantization of a system defined on a topologically non-trivial configuration space is ambiguous in that many inequivalent quantum systems are possible. This is the case for multiply connected spaces as well as for…
In this paper we discuss the unitary inequivalentness in quantum physics. Then based on some of the current outstanding problems in theoretical physics, we will show the important role of this concept to better understand the physical…
The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and…
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…