Related papers: Observables in quantum gravity
Gravity can be considered as an effective quantum field theory with reliable, but limited predictions. Though the influence of gravity on gauge and other interactions of elementary particles is still an open question. We calculate the…
Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity.…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
An observable on a quantum structure is any $\sigma$-homomorphism of quantum structures from the Borel $\sigma$-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the…
A Wilson loop is defined, in 4-D pure Einstein gravity, as the trace of the holonomy of the Christoffel connection or of the spin connection, and its invariance under the symmetry transformations of the action is showed (diffeomorphisms and…
We introduce $*$-structures on braided groups and braided matrices. Using this, we show that the quantum double $D(U_q(su_2))$ can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski…
In this paper DeWitt's formalism for field theories is presented; it provides a framework in which the quantization of fields possessing infinite dimensional invariance groups may be carried out in a manifestly covariant (non-Hamiltonian)…
We present a systematic study of one-loop quantum corrections in scalar effective field theories from a geometric viewpoint, emphasizing the role of field-space curvature and its renormalisation. By treating the scalar fields as coordinates…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
The microscopic theories of quantum gravity related to integrable lattice models can be constructed as special deformations of pure gravity. Each such deformation is defined by a second order differential operator acting on the coupling…
Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…
A simple diffeomorphism invariant theory of connections with the non-compact structure group R of real numbers is quantized. The theory is defined on a four-dimensional 'space-time' by an action resembling closely the self-dual Plebanski…
The Wick rotation provides the standard technique of computing Feynman diagrams by means of Euclidean propagators. Let us suppose that quantum fields in an interaction zone are really Euclidean. In contrast with the well-known Euclidean…
Quantum geometric maps, which relate SU(2) spin networks and Lorentz covariant projected spin networks, are an important ingredient of spin foam models (and tensorial group field theories) for 4-dimensional quantum gravity. We give a…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…