<i>Table of Integrals, Series, and Products</i>, edited by I. S. Gradshteyn and I. M. Ryzhik

Raeside, D. E.

doi:10.1118/1.594867

Cited by 19 publications

(22 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Investigations have been mainly restricted to renormalisation problems and to selfinteracting fields. To our knowledge, particular interaction effects between two different quantum fields have only been studied by Papastamatiou and Parker (1979), Birrell et al (1980 and Ford (1982). For further details compare Birrell (1981) and Birrell and Davies (1982).…”

Section: Introductionmentioning

confidence: 99%

Mutually interacting quantum fields in an expanding universe: decay of a massive particle

Audretsch¹,

Spangehl²

1985

Class. Quantum Grav.

View full text Add to dashboard Cite

The authors give an analysis of quantum field theory of mutually interacting fields in a 3-flat Robertson-Walker universe with regard to the questions: What are the measurable quantities? What is the related calculation scheme? The classical curved spacetime acts thereby as an external gravitational field, the influence of which is taken into account without any approximation. As a case study a mathematically rigorous calculation of the decay of a massive phi particle into two massless psi particles is given in first order of the ( lambda /a) phi psi 2 mutual interaction where a is the cosmic scale factor. The particles are conformally coupled scalar particles. The interaction picture and the in-out scheme based on an S-matrix approach are used. No renormalisation is needed. Because the external field is capable of producing pairs of massive phi particles from the vacuum, the specification of the outcome of the mutual interaction is based on the registration of massless particles in the out region. A detailed analysis of the corresponding added-up probability is given. It sheds some light on the imperfection of the usual in-out approach when applied to cosmological situations. The results are used to obtain a limit for the local applicability of flat spacetime results as cross section, decay rates etc. in a cosmological situation.

show abstract

Section: Introductionmentioning

confidence: 99%

Mutually interacting quantum fields in an expanding universe: decay of a massive particle

Audretsch¹,

Spangehl²

1985

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…We now recognise that the above equals E(I H (τ, Y(τ )), with I H (t, y) defined in (13). Using Lemma 1 we obtain J H (T, a) = J…”

Section: Lemmamentioning

confidence: 89%

Lower bound for the expected supremum of fractional brownian motion using coupling

Bisewski

2023

J. Appl. Probab.

View full text Add to dashboard Cite

We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index $H\in(0,1)$ over a (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms the Monte Carlo estimates based on very dense grids for $H\in(0,\tfrac{1}{2})$ . Additionally, we derive the Paley–Wiener–Zygmund representation of a linear fractional Brownian motion in the general case and give an explicit expression for the derivative of the expected supremum at $H=\tfrac{1}{2}$ in the sense of Bisewski, Dȩbicki and Rolski (2021).

show abstract

“…(6.621.3) from Gradshteyn and Ryzhik. 12 After a substantial amount of algebra, we find that the real part has the distribution 13…”

Section: Intermittent Signals Two Sensors (Cvγ Distribution)mentioning

confidence: 93%

Compound variance gamma distribution for modeling randomly scattered signals and detection at two sensors

Wilson

Ronan

Ostashev

2023

Automatic Target Recognition XXXIII

View full text Add to dashboard Cite

Decision metrics for automated target recognition and classification rely upon statistical distributions for the signal of interest and the background noise. This paper describes distribution models for situations in which an acoustic, RF, optical, or seismic signal is randomly scattered by the environment and received at one or two sensors, with the scattering strength varying randomly in space and time. A new distribution, called the compound variance gamma, is introduced, which applies to partially correlated data between two sensors with random scattering strength. This distribution reduces to several previously known scattering distributions as special cases. Calculation of receiver operating characteristic (ROC) curves using the new distribution is also discussed. A second new distribution, involving a product of modified Bessel functions, is also introduced to describe the magnitude of the cross product between a pair of sensors as needed to calculate the ROC curves. It is shown that the randomized scattering strength and correlation between the two sensors significantly impact signal detection.

show abstract

Table of Integrals, Series, and Products, edited by I. S. Gradshteyn and I. M. Ryzhik

Cited by 19 publications

References 0 publications

Mutually interacting quantum fields in an expanding universe: decay of a massive particle

Mutually interacting quantum fields in an expanding universe: decay of a massive particle

Lower bound for the expected supremum of fractional brownian motion using coupling

Compound variance gamma distribution for modeling randomly scattered signals and detection at two sensors

Contact Info

Product

Resources

About