Simple BRST quantization of general gauge models

It is shown that the BRST charge $Q$ for any gauge model with a Lie algebra symmetry may be decomposed as Q=\del+\del^{\dag}, \del^2=\del^{\dag 2}=0, [\del, \del^{\dag}]_+=0 provided dynamical Lagrange multipliers are used but without introducing other matter variables in \del than the gauge generators in $Q$. Furthermore, \del is shown to have the form \del=c^{\dag a}\phi_a (or $\phi'_ac^{\dag a}$) where $c^a$ are anticommuting expressions in the ghosts and Lagrange multipliers, and where the non-hermitian operators $\phi_a$ satisfy the same Lie algebra as the original gauge generators. By means of a bigrading the BRST condition reduces to \del|ph\hb=\del^{\dag}|ph\hb=0 which is naturally solved by c^a|ph\hb=\phi_a|ph\hb=0 (or c^{\dag a}|ph\hb={\phi'_a}^{\dag}|ph\hb=0). The general solutions are shown to have a very simple form.Comment: 18 pages, Late

Direct Acyclic Graph based Ledger for Internet of Things: Performance and Security Analysis

Direct Acyclic Graph (DAG)-based ledger and the corresponding consensus algorithm has been identified as a promising technology for Internet of Things (IoT). Compared with Proof-of-Work (PoW) and Proof-of-Stake (PoS) that have been widely used in blockchain, the consensus mechanism designed on DAG structure (simply called as DAG consensus) can overcome some shortcomings such as high resource consumption, high transaction fee, low transaction throughput and long confirmation delay. However, the theoretic analysis on the DAG consensus is an untapped venue to be explored. To this end, based on one of the most typical DAG consensuses, Tangle, we investigate the impact of network load on the performance and security of the DAG-based ledger. Considering unsteady network load, we first propose a Markov chain model to capture the behavior of DAG consensus process under dynamic load conditions. The key performance metrics, i.e., cumulative weight and confirmation delay are analysed based on the proposed model. Then, we leverage a stochastic model to analyse the probability of a successful double-spending attack in different network load regimes. The results can provide an insightful understanding of DAG consensus process, e.g., how the network load affects the confirmation delay and the probability of a successful attack. Meanwhile, we also demonstrate the trade-off between security level and confirmation delay, which can act as a guidance for practical deployment of DAG-based ledgers.Comment: accepted by IEEE Transactions on Networkin

Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This consequently provides the solution for the exponential $e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005), Myczkowce, Poland. 13 pages, 31 reference

Quasi-Metric Relativity

This is a survey of a new type of relativistic space-time framework; the so-called quasi-metric framework. The basic geometric structure underlying quasi-metric relativity is quasi-metric space-time; this is defined as a 4-dimensional differentiable manifold ${\cal N}$ equipped with two one-parameter families ${\bf {\bar g}}_t$ and ${\bf g}_t$ of Lorentzian 4-metrics parametrized by a global time function $t$. The metric family ${\bf {\bar g}}_t$ is found from field equations, whereas the metric family ${\bf g}_t$ is used to propagate sources and to compare predictions to experiments. A linear and symmetric affine connection compatible with the family ${\bf g}_t$ is defined, giving rise to equations of motion. Furthermore a quasi-metric theory of gravity, including field equations and local conservation laws, is presented. Just as for General Relativity, the field equations accommodate two independent propagating dynamical degrees of freedom. On the other hand, the particular structure of quasi-metric geometry allows only a partial coupling of space-time geometry to the active stress-energy tensor. Besides, the field equations are defined from projections of physical and geometrical tensors with respect to a ``preferred'' foliation of quasi-metric space-time into spatial hypersurfaces. The dynamical nature of this foliation makes the field equations unsuitable for a standard PPN-analysis. This implies that the experimental status of the theory is not completely clear at this point in time. The theory seems to be consistent with a number of cosmological observations and it satisfies all the classical solar system tests, though. Moreover, in its non-metric sector the new theory has experimental support where General Relativity fails or is irrelevant.Comment: 39 pages, no figures, LaTeX; v2: some points clarified; v3: connection changed; v4: extended and local conservation laws changed; v5: major revision; v6: accepted for publication in G&C; v7: must have non-universal gravitational coupling; v8: rewritten with fully coupled theory; v9: major revision (fully coupled theory abandoned