Quantization of Diffeomorphism-Invariant Theories with Fermions

We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose fiber is a sum of continuous unitary irreducible representations of the compact connected gauge group G, each representation appearing together with its dual. We consider theories whose classical configuration space is A x F, where A is the space of connections on P and F is the space of sections of F, regarded as a collection of Grassmann-valued fermionic fields. We construct the `quantum configuration space a x f as a completion of A x F. Using this we construct a Hilbert space L^2(a x f) for the quantum theory on which all automorphisms of P act as unitary operators, and determine an explicit `spin network basis' of the subspace L^2((a x f)/G) consisting of gauge-invariant states. We represent observables constructed from holonomies of the connection along paths together with fermionic fields and their conjugate momenta as operators on L^2((a x f)/G). We also construct a Hilbert space H_diff of diffeomorphism-invariant states using the group averaging procedure of Ashtekar, Lewandowski, Marolf, Mourao and Thiemann.Comment: 28 pages, latex, 7 ps-files (included) are needed to process the source fil

Muon g-2 through a flavor structure on soft SUSY terms

In this work we analyze the possibility to explain the muon anomalous magnetic moment discrepancy within theory and experiment through lepton flavor violation processes. We propose a flavor extended MSSM by considering a hierarchical family structure for the trilinear scalar Soft-Supersymmetric terms of the Lagranagian, present at the SUSY breaking scale. We obtain analytical results for the rotation mass matrix, with the consequence of having non-universal slepton masses and the possibility of leptonic flavour mixing. The one-loop supersymmetric contributions to the leptonic flavour violating process $\tau \to \mu\gamma$ are calculated in the physical basis, with slepton flavour mixed states, instead of using the well known Mass Insertion Method. We present the regions in parameter space where the muon g-2 problem is either entirely solved or partially reduced through the contribution of these flavor violating processes.Comment: 21 pages, 7 figures. Changes on version 3: In order to obtain the complete result for muon g-2 in the limit of non-flavor violation we added the terms given in the appendix. We redid the graphics and numerical analysis including these changes. We also corrected some typos and changed the order of figure

Does cash for school influence young women's behavior in the longer term ? evidence from Pakistan

The Punjab Female School Stipend Program, a female-targeted conditional cash transfer program in Pakistan, was implemented in response to gender gaps in education. An early evaluation of the program shows that the enrollment of eligible girls in middle school increased in the short term by nearly 9 percentage points. This paper uses regression discontinuity and difference-in-difference analyses to show that five years into the program implementation positive impacts do persist. Beneficiary adolescent girls are more likely to progress through and complete middle school and work less. There is suggestive evidence that participating girls delay their marriage and have fewer births by the time they are 19 years old. Girls who are exposed to the program later, and who are eligible for the benefits given in high school, increase their rates of matriculating into and completing high school. The persistence of impacts can potentially translate into gains in future productivity, consumption, inter-generational human capital accumulation and desired fertility. Lastly, there is no evidence that the program has negative spillover effects on educational outcomes of male siblings.Education For All,Primary Education,Tertiary Education,Gender and Education,Disability

An Invitation to Higher Gauge Theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institut

A pilot search for mm-wavelength recombination lines from emerging ionized winds in pre-planetary nebulae candidates

We report the results from a pilot search for radio recombination line (RRL) emission at millimeter wavelengths in a small sample of pre-planetary nebulae (pPNe) and young PNe (yPNe) with emerging central ionized regions. Observations of the H30\alpha, H31a, H39a, H41a, H48b, H49b, H51b, and H55g lines at 1 and 3mm have been performed with the IRAM 30 m radio telescope. These lines are excellent probes of the dense inner (<~150 au) and heavily obscured regions of these objects, where the yet unknown agents for PN-shaping originate. We detected mm-RRLs in three objects: CRL 618, MWC 922, and M 2-9. For CRL 618, the only pPN with previous published detections of H41a, H35a, and H30a emission, we find significant changes in the line profiles indicating that current observations are probing regions of the ionized wind with larger expansion velocities and mass-loss rate than ~29 years ago. In the case of MWC 922, we observe a drastic transition from single-peaked profiles at 3mm to double-peaked profiles at 1mm, which is consistent with maser amplification of the highest frequency lines; the observed line profiles are compatible with rotation and expansion of the ionized gas, probably arranged in a disk+wind system around a ~5-10 Msun central mass. In M 2-9, the mm-RRL emission appears to be tracing a recent mass outburst by one of the stars of the central binary system. We present the results from non-LTE line and continuum radiative transfer models, which enables us to constrain the structure, kinematics, and physical conditions (electron temperature and density) of the ionized cores of our sample. (abridged). We deduce mass-loss rates of ~1e-6-1e-7 Msun/yr, which are significantly higher than the values adopted by stellar evolution models currently in use and would result in a transition from the asymptotic giant branch to the PN phase faster than hitherto assumed.Comment: Accepted by Astronomy and Astrophysics. 28 pages, including figure

Asymptotics of Relativistic Spin Networks

The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the Spin Network evaluation. Finally we discuss the asymptotics of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification

Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity

In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF theories. In light of this new framework, we define a model for 4d gravity which includes the Immirzi parameter gamma. It reproduces the Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing models otherwise; in particular it does not require any rationality condition for gamma. We formulate the amplitudes both as BF simplicial path integrals with explicit non-commutative B variables, and in spin foam form in terms of Wigner 15j-symbols. Finally, we briefly discuss the correlation between neighboring simplices, often argued to be a problematic feature, for example, in the Barrett-Crane model.Comment: 26 pages, 1 figur

Spin Foam Models of Riemannian Quantum Gravity

Using numerical calculations, we compare three versions of the Barrett-Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for many triangulated 4-manifolds. In the version with modified face and edge amplitudes due to Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spin-zero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model.Comment: 23 pages LaTeX; this version to appear in Classical and Quantum Gravit