The reality conditions for the new canonical variables of General Relativity

We examine the constraints and the reality conditions that have to be imposed in the canonical theory of 4--d gravity formulated in terms of Ashtekar variables. We find that the polynomial reality conditions are consistent with the constraints, and make the theory equivalent to Einstein's, as long as the inverse metric is not degenerate; when it is degenerate, reality conditions cannot be consistently imposed in general, and the theory describes complex general relativity.Comment: 11

Spatial control of extreme ultraviolet light with opto-optical phase modulation

Extreme-ultraviolet (XUV) light is notoriously difficult to control due to its strong interaction cross-section with media. We demonstrate a method to overcome this problem by using Opto-Optical Modulation guided by a geometrical model to shape XUV light. A bell-shaped infrared light pulse is shown to imprint a trace of its intensity profile onto the XUV light in the far-field, such that a change in the intensity profile of the infrared pulse leads to a change in the shape of the far-field XUV light. The geometrical model assists the user in predicting the effect of a specific intensity profile of the infrared pulse, thus enabling a deterministic process

Macroscopic effects in noncollinear high-order harmonic generation.

We study two-color high-order harmonic generation using an intense driving field and its weak second harmonic, crossed under a small angle in the focus. Employing sum- and difference-frequency generation processes, such a noncollinear scheme can be used to measure and control macroscopic phase matching effects by utilizing a geometrical phase mismatch component, which depends on the noncollinear angle. We further show how spatial phase effects in the generation volume are mapped out into the far field allowing a direct analogy with temporal carrier envelope effects in attosecond pulse generation

Reality conditions for Ashtekar gravity from Lorentz-covariant formulation

We show the equivalence of the Lorentz-covariant canonical formulation considered for the Immirzi parameter $\beta=i$ to the selfdual Ashtekar gravity. We also propose to deal with the reality conditions in terms of Dirac brackets derived from the covariant formulation and defined on an extended phase space which involves, besides the selfdual variables, also their anti-selfdual counterparts.Comment: 14 page

Digital Epidemiology

Mobile, social, real-time: the ongoing revolution in the way people communicate has given rise to a new kind of epidemiology. Digital data sources, when harnessed appropriately, can provide local and timely information about disease and health dynamics in populations around the world. The rapid, unprecedented increase in the availability of relevant data from various digital sources creates considerable technical and computational challenges

New constraints for canonical general relativity

Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper 4-diffeos when the densitized dreibein, \tilE^a_i, is degenerate. The breakdown of 4-diffeo invariance appears to be due to the inability of the Ashtekar Hamiltonian to generate births and deaths of \tilE flux loops (leaving open the possibility that a new `causality condition' forbidding the birth of flux loops might justify the non-invariance of the theory). A fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived from Plebanski's action, is found to have constraints that are stronger than Ashtekar's for rank\tilE < 2. The corresponding Hamiltonian generates births and deaths of \tilE flux loops. It is argued that this implies a finite amplitude for births and deaths of loops in the physical states of quantum GR in the loop representation, thus modifying this (partly defined) theory substantially. Some of the new constraints are second class, leading to difficulties in quantization in the connection representation. This problem might be overcome in a very nice way by transforming to the classical loop variables, or the `Faraday line' variables of Newman and Rovelli, and then solving the offending constraints. Note that, though motivated by quantum considerations, the present paper is classical in substance.Comment: Version to appear in Nuclear Physics B. Discussion of 4-diffeo invariance, Dirac brackets improved. Proof of theorem connecting self-dual 2-forms and orthonormal tetrads replaced. Latex 57 pages, 7 uuencoded postscript figures. Uses macro psfig.tex available from this archive (and appended to this posting for your convenience). After latexing use dvips - not - dvi2ps to get postscript file

The Standard Model with gravity couplings

In this paper, we examine the coupling of matter fields to gravity within the framework of the Standard Model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti)self-dual or left-handed spin connection fields. It is known from the work of Ashtekar and others that such fields can furnish a complete description of gravity without matter. We show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C and T; and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly.Comment: Extended, and replaced with LaTex file. 25 Page

Localized qubits in curved spacetimes

We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |\psi_1>, along some spacetime path \Gamma from a spacetime point x_1 to another point x_2, what will the final quantum state |\psi_2> be at point x_2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe respectively the one-particle states of localized massive fermions and photons. In the WKB limit we show how one can isolate a two-dimensional quantum state which evolves unitarily along \Gamma. The quantum states for these two realizations are represented by a left-handed 2-spinor in the case of massive fermions and a four-component complex polarization vector in the case of photons. In addition we show how to obtain from this WKB approach a fully general relativistic description of gravitationally induced phases. We use this formalism to describe the gravitational shift in the COW 1975 experiment. In the non-relativistic weak field limit our result reduces to the standard formula in the original paper. We provide a concrete physical model for a Stern-Gerlach measurement of spin and obtain a unique spin operator which can be determined given the orientation and velocity of the Stern-Gerlach device and velocity of the massive fermion. Finally, we consider multipartite states and generalize the formalism to incorporate basic elements from quantum information theory such as quantum entanglement, quantum teleportation, and identical particles. The resulting formalism provides a basis for exploring precision quantum measurements of the gravitational field using techniques from quantum information theory.Comment: 53 pages, 7 figures; v2: published version with further corrections. v3: some references and equation typesetting fixe

Mitigation of Moral Hazard and Adverse Selection in Venture Capital Financing: The Influence of the Country’s Institutional Setting

A venture capitalist (VC) needs to trade off benefits and costs when attempting to mitigate agency problems in their investor-investee relationship. We argue that signals of ventures complement the VC’s capacity to screen and conduct a due diligence during the pre-investment phase, but its attractiveness may diminish in institutional settings supporting greater transparency. Similarly, whereas a VC may opt for contractual covenants to curb potential opportunism by ventures in the post-investment phase, this may only be effective in settings supportive of shareholder rights enforcement. Using an international sample of VC contracts, our study finds broad support for these conjectures. It delineates theoretical and practical implications for how investors can best deploy their capital in different institutional settings whilst nurturing their relationships with entrepreneurs

Clonal expansion and epigenetic reprogramming following deletion or amplification of mutant

IDH1 mutation is the earliest genetic alteration in low-grade gliomas (LGGs), but its role in tumor recurrence is unclear. Mutant IDH1 drives overproduction of the oncometabolite d-2-hydroxyglutarate (2HG) and a CpG island (CGI) hypermethylation phenotype (G-CIMP). To investigate the role of mutant IDH1 at recurrence, we performed a longitudinal analysis of 50 IDH1 mutant LGGs. We discovered six cases with copy number alterations (CNAs) at the IDH1 locus at recurrence. Deletion or amplification of IDH1 was followed by clonal expansion and recurrence at a higher grade. Successful cultures derived from IDH1 mutant, but not IDH1 wild type, gliomas systematically deleted IDH1 in vitro and in vivo, further suggestive of selection against the heterozygous mutant state as tumors progress. Tumors and cultures with IDH1 CNA had decreased 2HG, maintenance of G-CIMP, and DNA methylation reprogramming outside CGI. Thus, while IDH1 mutation initiates gliomagenesis, in some patients mutant IDH1 and 2HG are not required for later clonal expansions