Related papers: On parameterizations of the Nordheim function
In this paper we introduce new generalizations of the zeta function, the Tricomi functions; their main properties are studied. This opens the way to a deeper, better application of these functions both in the theory of special functions,…
We provide an axiomatic framework for Quantum Field Theory at finite temperature which implies the existence of general analyticity properties of the $ n $-point functions; the latter parallel the properties derived from the usual Wightman…
We introduce a stochastic particle system that corresponds to the Fokker-Planck equation with decay in the many-particles limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We investigate general properties of optical interferometry in stationary spacetimes and apply the obtained results focusing on quantum-optical experiments in near-Earth environments. We provide a rigorous expression for the…
In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…
Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
In a space of arbitrary dimensions, the effect of an external magnetic field on the vacuum of a quantized charged scalar field is studied for the field configuration in the form of a singular vortex. The zeta-function technique is used to…
In this paper, under the Riemann hypothesis, we study the Fourier analysis about the functions $\tilde{\Delta}(x)$ and $N(T)$ .
It is shown explicitly how the sign of Hardy's function $Z(t)$ depends on the parity of the zero-counting function $N(T)$. Two existing definitions of this function are analyzed, and some related problems are discussed.
The effect of the contribution of the vertical part of the real time path is studied completely in the case of two points functions. Indeed, this vertical part generally contributes in the calculation of a given graph. Moreover, this…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show that many properties which $\Ga(z)$ enjoys extend in a…
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
Rules of quantization and equations of motion for a finite-dimensional formulation of Quantum Field Theory are proposed which fulfill the following properties: a) both the rules of quantization and the equations of motion are covariant; b)…
Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that…
The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four point function. The equivalence between PCT theorem and {\it weak local commutativity}, due to Jost,…