Next Article in Journal
Cosmic-Ray Studies with Experimental Apparatus at LHC
Next Article in Special Issue
Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator
Previous Article in Journal
SAAE-DNN: Deep Learning Method on Intrusion Detection
Previous Article in Special Issue
An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers
Article

A Spectral Calculus for Lorentz Invariant Measures on Minkowski Space

School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
Symmetry 2020, 12(10), 1696; https://doi.org/10.3390/sym12101696
Received: 4 August 2020 / Revised: 30 September 2020 / Accepted: 10 October 2020 / Published: 15 October 2020
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications)
This paper presents a spectral calculus for computing the spectra of causal Lorentz invariant Borel complex measures on Minkowski space, thereby enabling one to compute their densities with respect to Lebesque measure. The spectra of certain elementary convolutions involving Feynman propagators of scalar particles are computed. It is proved that the convolution of arbitrary causal Lorentz invariant Borel complex measures exists and the product of such measures exists in a wide class of cases. Techniques for their computation in terms of their spectral representation are presented. View Full-Text
Keywords: Lorentz invariant complex measures; Minkowski space; spectral decomposition; measure convolution; measure product; Feynman propagator Lorentz invariant complex measures; Minkowski space; spectral decomposition; measure convolution; measure product; Feynman propagator
MDPI and ACS Style

Mashford, J. A Spectral Calculus for Lorentz Invariant Measures on Minkowski Space. Symmetry 2020, 12, 1696. https://doi.org/10.3390/sym12101696

AMA Style

Mashford J. A Spectral Calculus for Lorentz Invariant Measures on Minkowski Space. Symmetry. 2020; 12(10):1696. https://doi.org/10.3390/sym12101696

Chicago/Turabian Style

Mashford, John. 2020. "A Spectral Calculus for Lorentz Invariant Measures on Minkowski Space" Symmetry 12, no. 10: 1696. https://doi.org/10.3390/sym12101696

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop