Constrained Quantization on Symplectic Manifolds and Quantum Distribution Functions

A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar product on the reduced Hilbert space is investigated and possible solution of this problem is done. Generalization of the Gupta-Bleuler like conditions is done by the minimization of quadratic fluctuations of quantum constraints. The scheme for the construction of generalized coherent states is considered and relation with Berezin quantization is found. The quantum distribution functions are introduced and their physical interpretation is discussed.Comment: 42 page

Quantum derivation of the use of classical electromagnetic potentials in relativistic Coulomb excitation

We prove that a relativistic Coulomb excitation calculation in which the classical electromagnetic field of the projectile is used to induce transitions between target states gives the same target transition amplitudes, to all orders of perturbation theory, as would a calculation in which the interaction between projectile and target is mediated by a quantized electromagnetic field.Comment: 1 .zip file containing LaTex source plus three figures as .eps file

About Designing an Observer Pattern-Based Architecture for a Multi-objective Metaheuristic Optimization Framework

Multi-objective optimization with metaheuristics is an active and popular research field which is supported by the availability of software frameworks providing algorithms, benchmark problems, quality indicators and other related components. Most of these tools follow a monolithic architecture that frequently leads to a lack of flexibility when a user intends to add new features to the included algorithms. In this paper, we explore a different approach by designing a component-based architecture for a multi-objective optimization framework based on the observer pattern. In this architecture, most of the algorithmic components are observable entities that naturally allows to register a number of observers. This way, a metaheuristic is composed of a set of observable and observer elements, which can be easily extended without requiring to modify the algorithm. We have developed a prototype of this architecture and implemented the NSGA-II evolutionary algorithm on top of it as a case study. Our analysis confirms the improvement of flexibility using this architecture, pointing out the requirements it imposes and how performance is affected when adopting it.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The Gauge Fields and Ghosts in Rindler Space

We consider 2d Maxwell system defined on the Rindler space with metric ds^2=\exp(2a\xi)\cdot(d\eta^2-d\xi^2) with the goal to study the dynamics of the ghosts. We find an extra contribution to the vacuum energy in comparison with Minkowski space time with metric ds^2= dt^2-dx^2. This extra contribution can be traced to the unphysical degrees of freedom (in Minkowski space). The technical reason for this effect to occur is the property of Bogolubov's coefficients which mix the positive and negative frequencies modes. The corresponding mixture can not be avoided because the projections to positive -frequency modes with respect to Minkowski time t and positive -frequency modes with respect to the Rindler observer's proper time \eta are not equivalent. The exact cancellation of unphysical degrees of freedom which is maintained in Minkowski space can not hold in the Rindler space. In BRST approach this effect manifests itself as the presence of BRST charge density in L and R parts. An inertial observer in Minkowski vacuum |0> observes a universe with no net BRST charge only as a result of cancellation between the two. However, the Rindler observers who do not ever have access to the entire space time would see a net BRST charge. In this respect the effect resembles the Unruh effect. The effect is infrared (IR) in nature, and sensitive to the horizon and/or boundaries. We interpret the extra energy as the formation of the "ghost condensate" when the ghost degrees of freedom can not propagate, but nevertheless do contribute to the vacuum energy. Exact computations in this simple 2d model support the claim made in [1] that the ghost contribution might be responsible for the observed dark energy in 4d FLRW universe.Comment: Final version to appear in Phys. Rev. D. Comments on relation with energy momentum computations and few new refs are adde

Gauge equivalence in QCD: the Weyl and Coulomb gauges

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss's law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of $S$-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of ``standard'' perturbative states. The fact that the gauge-invariant chromoelectric field is not hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this nonhermiticity is taken into account, the ``extra'' vertices in Christ and Lee's Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this nonhermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.Comment: 25 page

Entanglement from longitudinal and scalar photons

The covariant quantization of the electromagnetic field in the Lorentz gauge gives rise to longitudinal and scalar photons in addition to the usual transverse photons. It is shown here that the exchange of longitudinal and scalar photons can produce entanglement between two distant atoms or harmonic oscillators. The form of the entangled states produced in this way is very different from that obtained in the Coulomb gauge, where the longitudinal and scalar photons do not exist. A generalized gauge transformation is used to show that all physically observable effects are the same in the two gauges, despite the differences in the form of the entangled states. An approach of this kind may be useful for a covariant description of the dynamics of quantum information processing.Comment: 12 pages, 1 figur

Finite temperature QCD

Engels J. Finite temperature QCD. In: Bleuler K, ed. Quarks and Nuclear Structure: Proceedings of the 3rd Klaus Erkelenz Symposium held at Bad Honnef, June 13–16,1983. Lecture Notes in Physics, 197. Berlin [u.a.]: Springer; 1984: 39-56.A review of finite temperature lattice calculations for quantum chromodynamics is given. We show how the thermodynamic quantities can be evaluated by Monte Carlo methods, once finite temperature field theory has been formulated on a lattice. The existing results for chemical potential zero and in quenched approximation are discussed. They exhibit a clear first order transition for SU(3) lattice QCD and probably a second order transition for SU(2) lattice QCD. The chiral and deconfinement transitions are coinciding in the quenched approximation

Using Comparative Preference Statements in Hypervolume-Based Interactive Multiobjective Optimization

International audienceThe objective functions in multiobjective optimization problems are often non-linear, noisy, or not available in a closed form and evolutionary multiobjective optimization (EMO) algorithms have been shown to be well applicable in this case. Here, our objective is to facilitate interactive decision making by saving function evaluations outside the "interesting" regions of the search space within a hypervolume-based EMO algorithm. We focus on a basic model where the Decision Maker (DM) is always asked to pick the most desirable solution among a set. In addition to the scenario where this solution is chosen directly, we present the alternative to specify preferences via a set of so-called comparative preference statements. Examples on standard test problems show the working principles, the competitiveness, and the drawbacks of the proposed algorithm in comparison with the recent iTDEA algorithm

Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as the pseudo-unitary ensemble. We obtain exact results for the nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing. This shows a level repulsion in marked distinction with an algebraic form in the Wigner surmise. We believe that this paves way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.Comment: 9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters on August 20, 200

Complex Ashtekar variables and reality conditions for Holst's action

From the Holst action in terms of complex valued Ashtekar variables additional reality conditions mimicking the linear simplicity constraints of spin foam gravity are found. In quantum theory with the results of You and Rovelli we are able to implement these constraints weakly, that is in the sense of Gupta and Bleuler. The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our result perfectly fit with recent developments of Rovelli and Speziale concerning Lorentz covariance within spin-form gravity.Comment: 24 pages, 2 picture