Vacuum Structures in Hamiltonian Light-Front Dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light-front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex

The embedding structure and the shift operator of the U(1) lattice current algebra

The structure of block-spin embeddings of the U(1) lattice current algebra is described. For an odd number of lattice sites, the inner realizations of the shift automorphism areclassified. We present a particular inner shift operator which admits a factorization involving quantum dilogarithms analogous to the results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected; version to appear in Lett.Math.Phy

Correlations of observables in chaotic states of macroscopic quantum systems

We study correlations of observables in energy eigenstates of chaotic systems of a large size $N$. We show that the bipartite entanglement of two subsystems is quite strong, whereas macroscopic entanglement of the total system is absent. It is also found that correlations, either quantum or classical, among less than $N/2$ points are quite small. These results imply that chaotic states are stable. Invariance of these properties under local operations is also shown.Comment: 5 pages, 2 figure

Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.Comment: 9 pages, 1 figure To be published in Physical Review

Robust coding of flow-field parameters by axo-axonal gap junctions between fly visual interneurons

Complex flight maneuvers require a sophisticated system to exploit the optic flow resulting from moving images of the environment projected onto the retina. In the fly's visual course control center, the lobula plate, 10 so-called vertical system (VS) cells are thought to match, with their complex receptive fields, the optic flow resulting from rotation around different body axes. However, signals of single VS cells are unreliable indicators of such optic flow parameters in the context of their noisy, texture-dependent input from local motion measurements. Here we propose an alternative encoding scheme based on network simulations of biophysically realistic compartmental models of VS cells. The simulations incorporate recent data about the highly selective connectivity between VS cells consisting of an electrical axo-axonal coupling between adjacent cells and a reciprocal inhibition between the most distant cells. We find that this particular wiring performs a linear interpolation between the output signals of VS cells, leading to a robust representation of the axis of rotation even in the presence of textureless patches of the visual surround

Reduction of Lie-Jordan Banach algebras and quantum states

A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the presence of quantum constraints. It is shown that the later corresponds to the particular instance of the reduction of Lie-Jordan Banach algebras with respect to a Lie-Jordan subalgebra as described in this paper. The space of states of the reduced Lie-Jordan Banach algebras is described in terms of equivalence classes of extensions to the full algebra and their GNS representations are characterized in the same way. A few simple examples are discussed that illustrates some of the main results

A Way Out of the Quantum Trap

We review Event Enhanced Quantum Theory (EEQT). In Section 1 we address the question "Is Quantum Theory the Last Word". In particular we respond to some of recent challenging staments of H.P. Stapp. We also discuss a possible future of the quantum paradigm - see also Section 5. In Section 2 we give a short sketch of EEQT. Examples are given in Section 3. Section 3.3 discusses a completely new phenomenon - chaos and fractal-like phenomena caused by a simultaneous "measurement" of several non-commuting observables (we include picture of Barnsley's IFS on unit sphere of a Hilbert space). In Section 4 we answer "Frequently Asked Questions" concerning EEQT.Comment: Replacement. Corrected affiliation. Latex, one .jpg figure. To appear in Proc. Conf. Relativistic Quantum Measurements, Napoli 1998, Ed. F. Petruccion

Carência de macronutrientes e de boro em plantas de juta (Corchorus capsularis L.), variedade roxa.

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