Open FRW model in Loop Quantum Cosmology is under consideration. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of k = −1 itis possible to construct a suitable loop which provides us with quantum scalar constraint originally introduced by Vandersloot [19]. The quantum scalar constraint operator with negative cosmolog...

Predicate abstraction is a major abstraction technique for the verification of software. Data is abstracted by means of Boolean variables, which keep track of predicates over the data. In many cases, the technique suffers from the fact that it requires at least one predicate for each iteration of a loop construct in the program. We propose to extract looping counterexamples from the abstract mo...

We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar’s new variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wavefunctions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simo...

We construct Bott-type Floer homology groups for the sym-plectic manifold (T S 1 ; can) and Bott-type Morse homology groups for the energy functional on the loop space of S 1. Both objects turn out to be isomorpic to the singular homology of the loop space of S 1. So far our objects depend on all choices involved, but the above isomorphism suggests further investigation to show independence of ...

We give two independent arguments why the classical membrane fields should be take values in a loop algebra. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N) for any N) that satisfies the algebraic s...

Open FRW model in Loop Quantum Cosmology is under consideration. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of k = −1 it is possible to construct a suitable loop which provides us with quantum scalar constraint originally introduced by Vandersloot [19]. Such an operator has correct geometrical interpretation. The...

At one loop, quantum kinks are described by a sum of harmonic oscillator Hamiltonians, and the ground state is just product states. Two-loop kink masses only known in integrable supersymmetric cases two-loop states have never been found. We find mass explicitly construct scalar field theory with an arbitrary nonderivative potential. use coherent operator which maps vacuum sector to sector, allo...

A bstract We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level ϕ 4 -theory and Yang-Mills theory. define a quantum perturbiner expansion that includes loop corrections from effective action formalism by identifying external source. Our method clearly shows how becomes an current generating function. Instead of using classic...

I present results for two-loop soft anomalous dimensions for heavy quark production which control soft-gluon resummation at next-to-next-to-leading-logarithm accuracy. I derive an explicit expression for the exact result and study it numerically for top quark production via e(+)e(-)-->tt, and I construct a surprisingly simple but very accurate approximation. I show that the two-loop soft anomal...

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-...