Renormalization of Poincare Transformations in Hamiltonian Semiclassical Field Theory

Semiclassical Hamiltonian field theory is investigated from the axiomatic point of view. A notion of a semiclassical state is introduced. An "elementary" semiclassical state is specified by a set of classical field configuration and quantum state in this external field. "Composed" semiclassical states viewed as formal superpositions of "elementary" states are nontrivial only if the Maslov isotropic condition is satisfied; the inner product of "composed" semiclassical states is degenerate. The mathematical proof of Poincare invariance of semiclassical field theory is obtained for "elementary" and "composed" semiclassical states. The notion of semiclassical field is introduced; its Poincare invariance is also mathematically proved.Comment: LaTeX, 40 pages; short version of hep-th/010307

Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework

Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler -- DeWitt constraint equations in terms of a single Master Equation. While the proposal has some promising abstract features, it was until now barely tested in known models. In this series of five papers we fill this gap, thereby adding confidence to the proposal. We consider a wide range of models with increasingly more complicated constraint algebras, beginning with a finite dimensional, Abelean algebra of constraint operators which are linear in the momenta and ending with an infinite dimensional, non-Abelean algebra of constraint operators which closes with structure functions only and which are not even polynomial in the momenta. In all these models we apply the Master Constraint Programme successfully, however, the full flexibility of the method must be exploited in order to complete our task. This shows that the Master Constraint Programme has a wide range of applicability but that there are many, physically interesting subtleties that must be taken care of in doing so. In this first paper we prepare the analysis of our test models by outlining the general framework of the Master Constraint Programme. The models themselves will be studied in the remaining four papers. As a side result we develop the Direct Integral Decomposition (DID) for solving quantum constraints as an alternative to Refined Algebraic Quantization (RAQ).Comment: 42 pages, no figure

Initial Conditions for Semiclassical Field Theory

Semiclassical approximation based on extracting a c-number classical component from quantum field is widely used in the quantum field theory. Semiclassical states are considered then as Gaussian wave packets in the functional Schrodinger representation and as Gaussian vectors in the Fock representation. We consider the problem of divergences and renormalization in the semiclassical field theory in the Hamiltonian formulation. Although divergences in quantum field theory are usually associated with loop Feynman graphs, divergences in the Hamiltonian approach may arise even at the tree level. For example, formally calculated probability of pair creation in the leading order of the semiclassical expansion may be divergent. This observation was interpretted as an argumentation for considering non-unitary evolution transformations, as well as non-equivalent representations of canonical commutation relations at different time moments. However, we show that this difficulty can be overcomed without the assumption about non-unitary evolution. We consider first the Schrodinger equation for the regularized field theory with ultraviolet and infrared cutoffs. We study the problem of making a limit to the local theory. To consider such a limit, one should impose not only the requirement on the counterterms entering to the quantum Hamiltonian but also the requirement on the initial state in the theory with cutoffs. We find such a requirement in the leading order of the semiclassical expansion and show that it is invariant under time evolution. This requirement is also presented as a condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur

Giant resonant light forces in microspherical photonics

Resonant light pressure effects can open new degrees of freedom in optical manipulation with microparticles, but they have been traditionally considered as relatively subtle effects. Using a simplified two-dimensional model of surface electromagnetic waves evanescently coupled to whispering gallery modes (WGMs) in transparent circular cavities, we show that under resonant conditions the peaks of the optical forces can approach theoretical limits imposed by the momentum conservation law on totally absorbing particles. Experimentally, we proved the existence of strong peaks of the optical forces by studying the optical propulsion of dielectric microspheres along tapered microfibers. We observed giant optical propelling velocities ∼0.45 mm s−1 for some of the 15-20 µm polystyrene microspheres in water for guided powers limited at ∼43 mW. Such velocities exceed previous observations by more than an order of magnitude, thereby providing evidence for the strongly enhanced resonant optical forces. We analyzed the statistical properties of the velocity distribution function measured for slightly disordered (∼1% size variations) ensembles of microspheres with mean diameters varying from 3 to 20 µm. These results demonstrate a principal possibility of optical sorting of microspheres with the positions of WGM resonances overlapped at the wavelength of the laser source. They can be used as building blocks of the lossless coupled resonator optical waveguides and various integrated optoelectronics devices

Status of NSLS-II booster

The National Synchrotron Light Source II is a third generation light source under construction at Brookhaven National Laboratory. The project includes a highly optimized 3 GeV electron storage ring, linac pre-injector and full-energy booster-synchrotron. Budker Institute of Nuclear Physics builds booster for NSLS-II. The booster should accelerate the electron beam continuously and reliably from minimal 170 MeV injection energy to maximal energy of 3.15 GeV and average beam current of 20 mA. The booster shall be capable of multi-bunch and single bunch operation. This paper summarizes the status of NSLS-II booster.Национальный источник синхротронного излучения II является синхротроном третьего поколения, созданным в Брукхевенской национальной лаборатории. Проект включает: высокооптимизированное накопительное кольцо на 3 ГэВ, линейный ускоритель и бустерный синхротрон на полную энергию. Институт ядерной физики им. Г.И. Будкера создает бустер для NSLS-II. Бустер должен надежно и непрерывно ускорять пучок электронов от минимальной энергии инжекции 170 МэВ до максимальной энергии 3,15 ГэВ с током пучка 20 мА. Бустер должен быть способен работать в односгустковом и многосгустковом режимах. Эта статья суммирует состояние дел по бустеру для NSLS-II.Національне джерело синхротронного випромінювання II є синхротроном третього покоління, створеним у Брукхевенській національній лабораторії. Проект включає: високооптимізоване накопичувальне кільце на 3 ГеВ, лінійний прискорювач і бустерний синхротрон на повну енергію. Інститут ядерної фізики ім. Г.І. Будкера створює бустер для NSLS-II. Бустер повинен надійно і безперервно прискорювати пучок електронів від мінімальної енергії інжекції 170 МеВ до максимальної енергії 3,15 ГеВ зі струмом пучка 20 мА. Бустер повинен бути здатний працювати в односгустковому і багатосгустковому режимах. Ця стаття підсумовує стан справ по бустеру для NSLS-II