Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P ! M, there is a canonicaìgeneralized measure' on the space A=G of smooth connections on P modulo gauge transformations. This allows one to deene a Hilbert space L 2 (A=G). Here we construct a set of vectors spanning L 2 (A=G). These vectors are described in terms of`spin networks': graphs embedded in M,...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

A major difficulty with conventional formulations of euclidean quantum gravity is the fact that the Einstein action I, can become arbitrarily negative [l]. This means that the path integral of exp( -In) does not converge. The problem persists for lattice formulations of gravity [2] and provides an obstacle to progress for calculations of anything other than the weak field limit [3]. A possible ...

This is the second paper concerning gauge-invariant coherent states for Loop Quantum Gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the abelian U(1) case encountered in the previous article. We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss-peaked in ga...

We present a six-dimensional Higgsless Standard Model with a realistic gauge sector. The model uses only the Standard Model gauge group SU(2)L × U(1)Y with the gauge bosons propagating in flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions, and the correct splitting between the W and Z gauge boson masses can be arranged by suitable choice...

We present a six-dimensional Higgsless Standard Model with a realistic gauge sector. The model uses only the Standard Model gauge group SU(2)L × U(1)Y with the gauge bosons propagating in flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions, and the correct splitting between the W and Z gauge boson masses can be arranged by suitable choice...

Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized N = 4 SYM theory, are considered in some detail. Duality between non-unitary field-theoretical representations and the unitary doubleton–type representations of the 4d conformal algebra su(2, 2) is formulated in terms of a Bogolyubov ...

The scale of mass generation for fermions (including neutrinos) and the scale for electroweak symmetry breaking (EWSB) can be generally bounded from above by the unitarity of scatterings involving longitudinal weak gauge bosons or their corresponding would-be Goldstone bosons. We reanalyze these scatterings for 2 → n processes (n > 2) with multiple gauge boson final states including the exact n...

The real space renormalization group is a powerful and elegant tool for the study of phase transitions in statistical systems. Concepts such as the universality of critical exponents are readily explained in terms of renormalization group flows in the vicinity of fixed points. In this paper we discuss how generalized Z, models provide a simple illustration of these ideas in a two-parameter coup...

We construct a twistor space action for N = 4 super Yang-Mills theory and show that it is equivalent to its four dimensional spacetime counterpart at the level of perturbation theory. We compare our partition function to the original twistor-string proposal, showing that although our theory is closely related to string theory, it is free from conformal supergravity. We also provide twistor acti...