Related papers: Quantizing the line element field
Let $E \subseteq \mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the…
The scalar product of two vectors with $K$ real components can be computed using two quantum channels, that is, information transmission lines in the form of spin-1/2 XX chains. Each channel has its own $K$-qubit sender and both channels…
It is first shown that the scalar product on any orthogonal space (V, g) allows one to define linear isomorphisms of the vector spaces of bivectors and 2-forms on V with the underlying vector spaces of the Lie algebra so(p, q) and its dual,…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
We study a model of quantum cosmology originating from a classical model of gravitation where a self interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical…
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an…
We construct the non-linear realisation of the semi-direct product of the very extended algebra A1+++ and its vector representation. This theory has an infinite number of fields that depend on a spacetime with an infinite number of…
We analyze the possibility of measuring the state of a movable mirror by using its interaction with a quantum field. We show that measuring the field quadratures allows to reconstruct the characteristic function corresponding to the mirror…
It is shown that if a metric in quantum gravity can be decomposed as a sum of classical and quantum parts then Einstein quantum gravity looks approximately like modified gravity with a nonminimal interaction between gravity and matter.
A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected…
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
We find the minimal number of independent preparations and measurements certifying the dimension of a classical or quantum system limited to $d$ states, optionally reduced to the real subspace. As a dimension certificate, we use the linear…
A basis of the ideal of the complement of a linear subspace in a projective space over a finite field is given. As an application, the second largest number of points of plane curves of degree $d$ over the finite field of $q$ elements is…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their…
Defects are a useful tool in the study of quantum field theories. This is illustrated in the example of two-dimensional conformal field theories. We describe how defect lines and their junction points appear in the description of symmetries…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
We regard a classical field as a medium and so the additional parameter, the velocity of a field,appears. If the one regard as a potential of same field then the self-energies of the fields became finite. Electromagnetic, mechanical,…
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation…