119302134
Generalized Spinfoams
We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kamiński-Kisielowski-Lewandowski (KKL) version where the foam is not dual to a triangulation. We study the Euclidean as well as the Lorentzian case. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. This constraint implies that boundary states admit a (quantum) geometrical interpretation in terms of polyhedra, generalizing the tetrahedral geometry of the simplicial case. We also point out that the general solution to this constraint (imposed weakly) depends on a quantum number rf in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when rf =0. We comment on the eventual physical relevance of rf , and the formal way to eliminate it.
119628044
On the Asymptotics of Quantum Group Spinfoam Model
Recently a quantum group deformation of EPRL spinfoam model was proposed in arXiv:1012.4216 by one of the authors, and in arXiv:1012.4784 by Fairbairn and Meusburger. It is interesting to study the high spin asymptotics of the quantum group spinfoam model, to see if it gives the discrete Einstein gravity with cosmological constant as its semiclassical limit. In this article we propose a new technique, which can simplify the analysis of the high spin asymptotics for quantum group spinfoam vertex amplitude. This technique can generalize the spinfoam asymptotic analysis developed by Barrett, et al to quantum group spinfoam. As a preparation of asymptotic analysis, we define and analyze the coherent states and coherent intertwiners for quantum group, which has certain "factorization properties". We show that in the high spin limit of quantum group spinfoam, many q-deformed noncommutative ingredients become classical and commutative. In particular, the squared norm of coherent intertwiner and the (Euclidean) vertex amplitude become integrals on classical group, while there are some additional terms (written in terms of classical group variables) make quantum group corrections to the usual (classical group) coherent intertwiner and vertex amplitude. These quantum group correction terms turn out to be proportional to the deformation parameter, which hopefully gives the cosmological term as its semiclassical limit.
5145645
Quantum dyanmics of loop quantum gravity
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, nonperturbative quantum theory for the Lorentzian gravitational field on a four-dimensional manifold. In this approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of "quantum Riemannian geometry", which is discrete at a fundamental scale. In the investigation of quantum dynamics, the classical expressions of constraints are quantized as operators. The quantum evolution is contained in the solutions of the quantum constraint equations. On the other hand, the semi-classical analysis has to be carried out in order to test the semiclassical limit of the quantum dynamics. 
In this thesis, the structure of the dynamical theory in loop quantum gravity is presented pedagogically. The outline is as follows: first we review the classical formalism of general relativity as a dynamical theory of connections. Then the kinematical Ashtekar-Isham-Lewandowski representation is introduced as a foundation of loop quantum gravity. We discuss the construction of a Hamiltonian constraint operator and the master constraint programme, for both the cases of pure gravity and matter field coupling. Finally, some strategies are discussed concerning testing the semiclassical limit of the quantum dynamics.
118608710
Spinfoam fermions
A serious shortcoming of spinfoam loop gravity is the absence of matter. See for instance [1, 2] and full references therein. Here we study a minimal coupling of the theory with a chiral fermion field and a Yang-Mills field. We find that the dynamical coupling of a fermion to quantum gravity is surprisingly simple in the spinfoam formalism. This result resonate with similar ones in early canonical loop theory [3, 4]: the naive fermion hamiltonian was found to be just the extension of the simple “shift” form [5] of the gravitational hamiltonian, to the open ends of the gravitational Faraday lines, which represent fermions. Here we find that in the spinfoams context the fermion dynamics is a natural extension of the gravitational amplitude to spin-networks with spin1 2 open-ends at the nodes. In the presence of fermions, it is then easy to add YangMills fields by promoting a global symmetry to a local symmetry. The dynamics can then be generated à la Zeld’hovic [6, 7] from fermion loops. For earlier studies on how to couple fermions to a discretized gravitational field, see [8–11]. For detailed studies of fermions in the loop quantum gravity canonical formalism, see [12–15]. On fermions in 3d, spinfoams and quantum cosmology and the effect of fermions on Holst gravity, see also [16–20].
17797254
HAMILTONIAN ANALYSIS OF n-DIMENSIONAL PALATINI GRAVITY WITH MATTER
We consider the Palatini formalism of gravity with cosmological constant Λ coupled to a scalar field ϕ in n dimensions. The n-dimensional Einstein equations with Λ can be derived by the variation of the coupled Palatini action provided n>2. The Hamiltonian analysis of the coupled action is carried out by a 1+(n-1) decomposition of the spacetime. It turns out that both Palatini action and Hilbert action lead to the same geometric dynamics in the presence of Λ and ϕ while the n-dimensional Palatini action could not give a dynamical formalism of connection directly.
118178605
SL(2,C) Chern–Simons theory, a non-planar graph operator, and 4D quantum gravity with a cosmological constant: Semiclassical geometry
Abstract We study the expectation value of a nonplanar Wilson graph operator in SL ( 2 , C ) Chern–Simons theory on S 3 . In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern–Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern–Simons action. This can be understood as arising from the relation between Chern–Simons theory on the boundary of a region, and a theory defined by an F 2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL ( 2 , C ) Chern–Simons theory in 3 dimensions with knotted graph defects.
122263475
Three triplets, paraquarks, and ''colored'' quarks
121149545
Generalization and Interpretation of Dirac's Positive-Energy Relativistic Wave Equation
We generalize Dirac's new equation so as to deacribe particles of mass m and arbitrary spin s. The same remarkable properties are found: positive energy, non-negative density, a conserved four-vector current, and the impossibility of minimal electromagnetic interaction. We show that the particles described by a subset of these equations are composites of two subparticles interacting by a relativistic action-at-a-distance interaction charactcrized by two harmonic oscillators. For these composite particles we find a linear relation between the square of the mass and the spin. We emphasizr that the essential content of the generalized new Dirac equation is that it constitutes an example of a convariant solution for two interacting particles, and provides an explicit examaple of a new quantal subdynamics distinct from the (classical) front relativistic dynamics of Dirac. (auth)
119892209
Finite quantum electrodynamics: A field theory using an indefinite metric
A finite relativistic field theory of quantum electrodynamics is formulated; the theory involves as an essential element the use of an indefinite metric to remove the divergences. Two auxiliary fermion fields with anticommutation relations of opposite sign from the normal fermion field (electron) are coupled with the electron to the electromagnetic field in such a manner that any matrix element, calculated by a perturbation expansion, is finite. Although the new Lagrangian is not explicitly gauge invariant, the electromagnetic field is quantized by a method that yields a propagator in the true Landau gauge, and it is shown that this is sufficient to insure that the physical vector particles are zero-mass transverse quanta (i.e., photons). The physical electron mass and the fine-structure constant are put into the theory, leaving only the masses of the two auxiliary fields as parameters. The effects of mass and charge renormalization are calculated (the former using a technique involving a Taylor expansion in the mass), and are required to be small so that there is no explicit contradiction to the validity of the perturbation expansion. The anomalous magnetic moment of the electron and the differential and total cross sections for Compton scattering are calculated and compared with experiment. A range of the auxiliary mass parameters is found for which the predictions agree with experiment and for which the expansion criteria are satisfied. Thus, a finite quantum electrodynamics is accomplished.
123307684
Hadronic regge sequences as primitive realizations of SL(3,R) symmetry☆
Abstract Four primitive infinite dimensional unitary representations of the group of rotations and deformations - SL(3,R) - are constructed and associated with the four Regge trajectories: π, ϱ, N, Δ. The model predicts E2 transition moments and a power law for E versus j consistent with the Chew-Frautschi relation E∼j 1 2 .
121268649
Comment on "Stigma of a Dirac Particle in an Even Environment"