Related papers: Jordan Form and Quantum Tomography

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…

In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree $\geq 3$ we show that any finite-dimensional representation is completely reducible and, depending…

In this paper we show that any linear vector field $\mathcal{X}$ on a connected Lie group $G$ admits a Jordan decomposition and the recurrent set of the associated ow of automorphisms is given as the intersection of the fixed points of the…

We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general…

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…

We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different concepts.…

In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate…

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. Two types of contributing pairs of orbits were…

We investigate the proportional relationships for spectrums and for SJNFs (Standard Jordan Normal Forms) of the matrices constructed from coefficient matrices of two SLOCC (stochastic local operations and classical communication) equivalent…

Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…

It is well known that the Jordan and Einstein frames are equivalent to each other in classical Brans-Dicke theory, provided that one and the same metric is employed for the physical space-time. Nevertheless, it is shown in this paper by…

In the framework of a general scalar-tensor theory, we investigate the equivalence between two different parametrizations of fields that are commonly used in cosmology - the so-called Jordan frame and Einstein frame. While it is clear that…

Using a global rotation by theta about the z-axis in the spin sector of the Jordan-Wigner transformation rotates Pauli matrices X and Y in the x-y-plane, while it adds a global complex phase to fermionic quantum states that have a fixed…

Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting vector representation is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum…

We study the question of whether two frames of a given physical theory are equivalent or not in the presence of quantum corrections. By using field theory arguments we claim that equivalence is broken in the presence of anomalous symmetries…

Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…

We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct…

Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative…

Theory of the quantum quartic oscillator is developed with close attention to the energy cutoff one needs to impose on the system in order to approximate the smallest eigenvalues and corresponding eigenstates of its Hamiltonian by…

In 2003 Peter Cameron introduced the concept of a Jordan scheme and asked whether there exist Jordan schemes which are not symmetrisations of coherent configurations (proper Jordan schemes). The question was answered affirmatively by the…