Related papers: Asymptotic Limits and Sum Rules for the Quark Prop…
For gauge field propagators, the asymptotic behavior is obtained in all directions of the complex $k^2$-plane, and for general, linear, covariant gauges. Asymptotically free theories are considered. Except for coefficients, the functional…
It is well known that the long-range nature of the Coulomb interaction makes the definition of asymptotic ``in'' and ``out'' states of charged particles problematic in quantum field theory. In particular, the notion of a simple particle…
We investigate the nonperturbative behaviour of the quark propagator in axial gauge using a truncation of the Dyson-Schwinger equations which respects the Ward-Takahashi identity and multiplicative renormalisability. We demonstrate that…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.
This talk will summarise the progress we have made in our programme to both characterise and construct charges in gauge theories. As an application of these ideas we will see how the dominant glue surrounding quarks, which is responsible…
Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…
The structure of the quark propagator in momentum space is explored taking into account non-perturbative QCD dynamics constraints for the quark spectral densities derived previously. We assume that the scalar and vector component of the…
The asymptotic behavior as t\to\infty and r\to\infty of the hard-thermal-loop propagator D^{\mu\nu}(t,r) is computed in the Coulomb gauge. The asymptotic falloff is always a power law though generally different in the deep time-like and…
In a previous article we have show that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized…
Quantum Chromodynamics (QCD), the gauge field theory of the Strong Interaction, has specific features, asymptotic freedom and confinement, which determine the behaviour of quarks and gluons in particle reactions at high and at low energy…
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
We present progress in the QCD analysis of the Bjorken sum rule at low momentum transfers. We study asymptotic structure of the perturbative QCD expansion at low $Q^2$ scales based on analysis of recent accurate data on the Bjorken sum rule…
We provide an asymptotic expansion for $\sum_{k=1}^n \left\{\sqrt{k}\right\}$. In the same spirit, we discuss the case of n-th root and it relation to special values of Riemman's zeta function.
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
We summarize the main results of a microscopically based kinetic theory, applicable to open quantum point contacts (QPCs) driven up to high fields. The governing role of gauge invariance -- and the many-body sum rules for the electron gas…
We have investigated a closed set of equations for the quark propagator, which has been obtained earlier within a new, nonperturbative approach to two-dimencional covariant gauge QCD. It is shown that this theory implies quark confinement…
This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate of the remainder term of the asymptotic expansion of the sums…