What do you mean by delta function to be lorentz invariant?
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In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. ... While the components of vectors and tensors are in general altered under Lorentz transformations, Lorentz scalars remain unchanged.
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The delta function is a generalized function that can be defined as the limit of a class of delta sequences. ... The action of on , commonly denoted or , then gives the value at 0 of for any function . In engineering contexts, the functional nature of the delta function is often suppressed
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