Fourier Transforms of Lorentz Invariant Functions
Alexander Wurm, Nurit Krausz, Cecile DeWitt-Morette, Marcus Berg
TL;DR
This paper computes Fourier transforms of Lorentz invariant functions in Minkowski space across various dimensions, providing explicit results for 1+1 and 1+2 dimensions and general formulas for higher dimensions.
Contribution
It offers a detailed method for Fourier transforming Lorentz invariant functions in Minkowski space, including explicit solutions in low dimensions and general formulas for higher dimensions.
Findings
Explicit Fourier transforms in 1+1 and 1+2 dimensions.
General formulas for Fourier transforms in 1+n dimensions.
Methodology for direct integration of Lorentz invariant functions.
Abstract
Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given.
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