Unitary Invariance Research Articles

The effect of “anthihypertensive folk medicine” on the dietary intake of minerals in the elderly: Zelma A. Payne, Spelman College and W. Dallas Hall 350 Spelman Lane, Southwest - Atlanta, Georgia 30314

Given two two-qubit pure states characterized by their Schmidt numbers we investigate an optimal strategy to convert the states between themselves with respect to their local unitary invariance. We discuss the efficiency of this transformation and its connection to LOCC convertibility properties between two single-copy quantum states. As an illustration of the investigated transformations we present a communication protocol where in spite of all expectations a shared maximally entangled pair between two participants is the worst quantum resource.

Hypertension specialist training program: Anne Griffin Perry, Saint Louis University, Department of Nursing, 3525 Caroline Street, Saint Louis, Missouri 63104; Judith H. Carlson; Carol A. Craft; H. Mitchell Perry, Jr.

Given two two-qubit pure states characterized by their Schmidt numbers we investigate an optimal strategy to convert the states between themselves with respect to their local unitary invariance. We discuss the efficiency of this transformation and its connection to LOCC convertibility properties between two single-copy quantum states. As an illustration of the investigated transformations we present a communication protocol where in spite of all expectations a shared maximally entangled pair between two participants is the worst quantum resource.

Unitary Invariance in Algebraic Algebras

Unitary Invariance in Algebraic Algebras

Unitary invariance in algebraic algebras

A structure theorem is obtained for subspaces invariant under conjugation by the unitary group of a prime algebraic algebra over an infinite field. For an invariant subalgebra W, it is shown that either W is central, W contains an ideal, or the ring satisfies the standard identity of degree eight. Also, for prime algebras not satisfying such an identity, the unitary group is not solvable.

Quantization of relativistic systems with boson and fermion first- and second-class constraints

The general solution for the S matrix of an arbitrary Hamilton system with boson and fermion first- and second-class constraints of general form is obtained. Additional diagrams arise securing unitary and gauge invariance of the theory: the many-particle interaction of fermion and boson ghosts. The generalized Ward identities are obtained.

Uniqueness of the positive energy parafermion field

In t953, Green [1] proposed that the usual anticommutation relations of Fermi-Dirac statistics be generalized. He proposed new relations which are satisfied by the Fermi-Dirac creation and annihilation operators but admit additional representations, each of which can also be given a particle interpretation. These particles are called parafermions. For n degrees of freedom it has been shown [4] that the representations of Green's relations are just the representations of SO(2n + 1, R), which are well known. For infinitely many degrees of freedom the situation is more complicated. Reducible representations may be constructed by the use of Green's ansatz [1 ; 2] from which certain standard irreducible representations are chosen. The uniqueness of these standard representations is usually discussed in terms of the existence of a unique vacuum vector which is annihilated by all annihilation operators. The purpose of this paper is to obtain uniqueness results relating to unitary invariance as was done for ordinary particles by Segal [5, Theorems 1, 2, 3] and Weinless [6, Theorem 2.1].

Closure procedures in crystal field theory

The group symmetry and unitary invariance of certain projection operators are discussed, and it is pointed out that closure approximations impose particular group symmetries on the intermediate states projection operators of second-order perturbation theory. The unitary invariance property of projection operators enables evaluation of second-order crystal field effects for a term without detailed knowledge of the crystal field levels of the perturbing terms. The latter result is applied in some numerical calculations for the rare earth Pr3+.

On generalized field quantization procedures

It is shown that a quantization procedure given by Parks is either identical with the method of Roman and Aghassi or with an obvious alteration of the para field theory depending on the definition of the number operator. Next, by an appropriate change of the para commulation relations for the creation and annihilation operators we define a whole set of such theories which includes the para field theory themselves and the method of Parks. However, by the requirement of unitary invariance of the corresponding commulation relations all these theories except the para field theory may be ruled out.