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In the ISQ, 1/ε 0 converts or scales electric flux density, D, to the corresponding electric field, E (the latter has dimension of force per charge), while in the Gaussian system, electric flux density is the same quantity as electric field strength in free space aside from a dimensionless constant factor.
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form = () ...
Common integrals in quantum field theory are all variations and generalizations of Gaussian integrals to the complex plane and to multiple dimensions. [1]: 13–15 Other integrals can be approximated by versions of the Gaussian integral. Fourier integrals are also considered.
The electromagnetic stress–energy tensor in the International System of Quantities (ISQ), which underlies the SI, is [1] = [], where is the electromagnetic tensor and where is the Minkowski metric tensor of metric signature (− + + +) and the Einstein summation convention over repeated indices is used.
Owen [1] has an extensive list of Gaussian-type integrals; only a subset is given below. Indefinite integrals
The definitions above are according to the International System of Quantities (ISQ) upon which the SI is based. However, many tables of magnetic susceptibility give the values of the corresponding quantities of the CGS system (more specifically CGS-EMU , short for electromagnetic units, or Gaussian-CGS ; both are the same in this context).
A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite.The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime.
A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.