The three fundamental geometric components of YangMills theory -gauge field, gauge fixing and ghost fieldare unified in a new object: an extended connection in a properly chosen principal fiber bundle. To do this, it is necessary to generalize the notion of gauge fixing by using a gauge fixing connection instead of a section. From the equations for the extended connections curvature, we derive ...

We apply Dirac’s gauge fixing procedure to (2+1)-gravity with vanishing cosmological constant. For general gauge fixing conditions based on two point particles, this yields explicit expressions for the Dirac bracket. We explain how gauge fixing is related to the introduction of an observer into the theory and show that the Dirac bracket is determined by a classical dynamical r-matrix. Its two d...

Gouranga C Nayak ∗ 1 Department of Physics, University of Arizona, Tucson, AZ 85721, USA Abstract In this paper we derive a gauge fixing identity by varying the covariant gauge fixing term in Z[A, J, η, η̄] in the background field method of QCD in pure gauge. Using this gauge fixing identity we establish a relation between Z[J, η, η̄] in QCD and Z[A, J, η, η̄] in background field method of QCD in ...

In computer science fixpoints play a crucial role. Most often least and greatest fixpoints are sufficient. However there are situations where other ones are needed. In this paper we study, on an algebraic base, a special fixpoint of the function f (x) = a · x that describes infinite iteration of an element a. We show that the greatest fixpoint is too imprecise. Special problems arise if the ite...

Bitcoin has been hailed as a new payment mechanism, and is currently accepted by millions of users. One of the major drawbacks of Bitcoin is the resource intensive Proof-of-Work computation. Proof-of-Work is used to establish the blockchain, but this proof of work does not bring any benefits and arguably is a waste of energy. To use these available resources in a more meaningful way, several al...

Concurrency bugs are widespread in multithreaded programs. Fixing them is time-consuming and error-prone. We present CFix, a system that automates the repair of concurrency bugs. CFix works with a wide variety of concurrency-bug detectors. For each failure-inducing interleaving reported by a bug detector, CFix first determines a combination of mutual-exclusion and order relationships that, once...

ion to improve programming productivity, which usually compromises target program performance. Transformation-based generators widen the quandary through deep factorization of operators and operands to amplify expressive power, but this explodes the search space. My hypothesis is that existing architectures are inadequate to achieve simultaneously high levels of abstraction, high performance ta...