Related papers: Colorless operators in a non-associative quantum t…
Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…
There are self-adjoint operators which determine both spectral and semispectral measures. These measures have very different commutativity and covariance properties. This fact poses a serious question on the physical meaning of such a…
We describe realizations of the color analogue of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to…
Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of…
While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, there does not exist an analogous operator representing general quantum correlations…
We realize, for the first time, a non-Abelian gauge theory with both gauge and matter fields on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered…
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator…
The commutation relations for bosons are field independent, and can be reliably inferred from the definition of creation and annihilation operators. Here, the commutation relations are assumed known, and the quantum electrodynamics…
Following the work of Dine and Seiberg for SU(2), we study the leading irrelevant operators on the moduli space of N=4 supersymmetric SU(N) gauge theory. These operators are argued to be one-loop exact, and are explicitly computed.
A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…
Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional…
We are focused on the idea that observables in quantum physics are a bit more than just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
The paper argues that far from challenging - or even refuting - Bohm's quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to…
We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of positive-operator-valued measure decompositions. The latter arise from integrals over families of…
This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown…
We present classes of nonassociative algebras whose associator satisfies invariance conditions given by the action of the 3 order symmetric group. Amongst these algebras we find the wellknown Pre Lie or Vinberg algebras and the Lie…
A three-dimensional $q$-Lie algebra of $SU_q(2)$ is realized in terms of first- and second-order differential operators. Starting from the $q$-Lie algebra one has constructed a left-covariant differential calculus on the quantum group. The…
We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom and it is represented by a quantum shifting superoperator that maps quantum…
We investigate properties of the color space of $SU(N_c)$ gauge theories in the limit of small number of colors $(N_c \to 0)$ and large number of flavors. More generally, we introduce a rescaling of $\alpha_s$ and $n_f$ which assigns a…