178 research outputs found

### Mickelsson algebras and Zhelobenko operators

We construct a family of automorphisms of Mickelsson algebra, satisfying
braid group relations. The construction uses 'Zhelobenko cocycle' and includes
the dynamical Weyl group action as a particular case

### Information-disturbance tradeoff in estimating a maximally entangled state

We derive the amount of information retrieved by a quantum measurement in
estimating an unknown maximally entangled state, along with the pertaining
disturbance on the state itself. The optimal tradeoff between information and
disturbance is obtained, and a corresponding optimal measurement is provided.Comment: 4 pages. Accepted for publication on Physical Review Letter

### Dynamical Ambiguities in Singular Gravitational Field

We consider particle dynamics in singular gravitational field. In 2d
spacetime the system splits into two independent gravitational systems without
singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but
the corresponding symmetry transformations are not defined globally.
Quantization leads to ambiguity. By including singularity one can get the
global $SO(2.1)$ symmetry. Quantization in this case leads to unique quantum
theory.Comment: 7 pages, latex, no figures, submitted for publicatio

### On the fidelity of two pure states

The fidelity of two pure states (also known as transition probability) is a
symmetric function of two operators, and well-founded operationally as an event
probability in a certain preparation-test pair. Motivated by the idea that the
fidelity is the continuous quantum extension of the combinatorial equality
function, we enquire whether there exists a symmetric operational way of
obtaining the fidelity. It is shown that this is impossible. Finally, we
discuss the optimal universal approximation by a quantum operation.Comment: LaTeX2e, 8 pages, submitted to J. Phys. A: Math. and Ge

### New Generalized Verma Modules and Multilinear Intertwining Differential Operators

The present paper contains two interrelated developments. First, are proposed
new generalized Verma modules. They are called k-Verma modules, k\in N, and
coincide with the usual Verma modules for k=1. As a vector space a k-Verma
module is isomorphic to the symmetric tensor product of k copies of the
universal enveloping algebra U(g^-), where g^- is the subalgebra of lowering
generators in the standard triangular decomposition of a simple Lie algebra g =
g^+ \oplus h \oplus g^- . The second development is the proposal of a procedure
for the construction of multilinear intertwining differential operators for
semisimple Lie groups G . This procedure uses k-Verma modules and coincides for
k=1 with a procedure for the construction of linear intertwining differential
operators. For all k central role is played by the singular vectors of the
k-Verma modules. Explicit formulae for series of such singular vectors are
given. Using these are given explicitly many new examples of multilinear
intertwining differential operators. In particular, for G = SL(2,R) are given
explicitly all bilinear intertwining differential operators. Using the latter,
as an application are constructed (n/2)-differentials for all n\in 2N, the
ordinary Schwarzian being the case n=4. As another application, in a Note Added
we propose a new hierarchy of nonlinear equations, the lowest member being the
KdV equation.Comment: 30 pages, plain TEX with harvmac; corrected misprint

### Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras

This paper completes a series devoted to explicit constructions of
finite-dimensional irreducible representations of the classical Lie algebras.
Here the case of odd orthogonal Lie algebras (of type B) is considered (two
previous papers dealt with C and D types). A weight basis for each
representation of the Lie algebra o(2n+1) is constructed. The basis vectors are
parametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the
matrix elements of generators of o(2n+1) in this basis are given. The
construction is based on the representation theory of the Yangians. A similar
approach is applied to the A type case where the well-known formulas due to
Gelfand and Tsetlin are reproduced.Comment: 29 pages, Late

### Physical Vacuum Properties and Internal Space Dimension

The paper addresses matrix spaces, whose properties and dynamics are
determined by Dirac matrices in Riemannian spaces of different dimension and
signature. Among all Dirac matrix systems there are such ones, which nontrivial
scalar, vector or other tensors cannot be made up from. These Dirac matrix
systems are associated with the vacuum state of the matrix space. The simplest
vacuum system realization can be ensured using the orthonormal basis in the
internal matrix space. This vacuum system realization is not however unique.
The case of 7-dimensional Riemannian space of signature 7(-) is considered in
detail. In this case two basically different vacuum system realizations are
possible: (1) with using the orthonormal basis; (2) with using the
oblique-angled basis, whose base vectors coincide with the simple roots of
algebra E_{8}.
Considerations are presented, from which it follows that the least-dimension
space bearing on physics is the Riemannian 11-dimensional space of signature
1(-)& 10(+). The considerations consist in the condition of maximum vacuum
energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio

### The BV-algebra structure of W_3 cohomology

We summarize some recent results obtained in collaboration with J. McCarthy
on the spectrum of physical states in $W_3$ gravity coupled to $c=2$ matter. We
show that the space of physical states, defined as a semi-infinite (or BRST)
cohomology of the $W_3$ algebra, carries the structure of a BV-algebra. This
BV-algebra has a quotient which is isomorphic to the BV-algebra of polyvector
fields on the base affine space of $SL(3,C)$. Details have appeared elsewhere.
[Published in the proceedings of "Gursey Memorial Conference I: Strings and
Symmetries," Istanbul, June 1994, eds. G. Aktas et al., Lect. Notes in Phys.
447, (Springer Verlag, Berlin, 1995)]Comment: 8 pages; uses macros tables.tex and amssym.def (version 2.1 or later

### High energy QCD as a completely integrable model

We show that the one-dimensional lattice model proposed by Lipatov to
describe the high energy scattering of hadrons in multicolor QCD is completely
integrable. We identify this model as the XXX Heisenberg chain of noncompact
spin $s=0$ and find the conservation laws of the model. A generalized Bethe
ansatz is developed for the diagonalization of the hamiltonian and for the
calculation of hadron-hadron scattering amplitude.Comment: Latex style, 16 pages, ITP-SB-94-1

### Quantum state estimation and large deviations

In this paper we propose a method to estimate the density matrix \rho of a
d-level quantum system by measurements on the N-fold system. The scheme is
based on covariant observables and representation theory of unitary groups and
it extends previous results concerning the estimation of the spectrum of \rho.
We show that it is consistent (i.e. the original input state \rho is recovered
with certainty if N \to \infty), analyze its large deviation behavior, and
calculate explicitly the corresponding rate function which describes the
exponential decrease of error probabilities in the limit N \to \infty. Finally
we discuss the question whether the proposed scheme provides the fastest
possible decay of error probabilities.Comment: LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one
new subsection (4.1) and another (4.2 was 4.1 in the previous version)
completely rewritten. Minor changes in Sect. 2 and 3. Typos corrected.
References added. Accepted for publication in Rev. Math. Phy

- âŠ