From covariant to canonical formulations of discrete gravity

Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits exact gauge symmetries -- we derive local and first class constraints for arbitrary triangulated Cauchy surfaces. These constraints have a clear geometric interpretation and are a first step towards obtaining anomaly--free constraint algebras for canonical lattice gravity. Taking higher order dynamics into account the symmetries of the action are broken. This results in consistency conditions on the background gauge parameters arising from the lowest non--linear equations of motion. In the canonical framework the constraints to quadratic order turn out to depend on the background gauge parameters and are therefore pseudo constraints. These considerations are important for connecting path integral and canonical quantizations of gravity, in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version + updated references

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Chaotic quantum ratchets and filters with cold atoms in optical lattices: properties of Floquet states

Recently, cesium atoms in optical lattices subjected to cycles of unequally-spaced pulses have been found to show interesting behavior: they represent the first experimental demonstration of a Hamiltonian ratchet mechanism, and they show strong variability of the Dynamical Localization lengths as a function of initial momentum. The behavior differs qualitatively from corresponding atomic systems pulsed with equal periods, which are a textbook implementation of a well-studied quantum chaos paradigm, the quantum delta-kicked particle (delta-QKP). We investigate here the properties of the corresponding eigenstates (Floquet states) in the parameter regime of the new experiments and compare them with those of the eigenstates of the delta-QKP at similar kicking strengths. We show that, with the properties of the Floquet states, we can shed light on the form of the observed ratchet current as well as variations in the Dynamical Localization length.Comment: 9 pages, 9 figure

Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update

QED effective action at finite temperature

The QED effective Lagrangian in the presence of an arbitrary constant electromagnetic background field at finite temperature is derived in the imaginary-time formalism to one-loop order. The boundary conditions in imaginary time reduce the set of gauge transformations of the background field, which allows for a further gauge invariant and puts restrictions on the choice of gauge. The additional invariant enters the effective action by a topological mechanism and can be identified with a chemical potential; it is furthermore related to Debye screening. In concordance with the real-time formalism, we do not find a thermal correction to Schwinger's pair-production formula. The calculation is performed on a maximally Lorentz covariant and gauge invariant stage.Comment: 9 pages, REVTeX, 1 figure, typos corrected, references added, final version to appear in Phys. Rev.

From the discrete to the continuous - towards a cylindrically consistent dynamics

Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum gravity we propose a coarse graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme towards this end. A crucial role in this coarse graining scheme is played by embedding maps that allow the interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as a choice of embedding maps will determine a truncation of the renormalization flow.Comment: 22 page

Scattering through a straight quantum waveguide with combined boundary conditions

Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered using stationary scattering theory. The existence of a matching conditions solution at x=0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.Comment: 26 pages, 3 figure

Monitoring induced gene expression of single cells in a multilayer microchip

We present a microfluidic system that facilitates long-term measurements of single cell response to external stimuli. The difficulty of addressing cells individually was overcome by using a two-layer microfluidic device. The top layer is designed for trapping and culturing of cells while the bottom layer is employed for supplying chemical compounds that can be transported towards the cells in defined concentrations and temporal sequences. A porous polyester membrane that supports transport and diffusion of compounds from below separates the microchannels of both layers. The performance and potential of the device are demonstrated using human embryonic kidney cells (HEK293) transfected with an inducible gene expression system. Expression of a fluorescent protein (ZsGreen1-DR) is observed while varying the concentration and exposure time of the inducer tetracycline. The study reveals the heterogeneous response of the cells as well as average responses of tens of cells that are analyzed in parallel. The microfluidic platform enables systematic studies under defined conditions and is a valuable tool for general single cell studies to obtain insights into mechanisms and kinetics that are not accessible by conventional macroscopic methods. Figure A two-layer microfluidic device is presented that facilitates measurements of single cell response to external stimul