Scale Invariance Vs. Conformal Invariance
While it is possible for a quantum field theory to be scale invariant but not conformally-invariant, examples are rare . For this reason, the terms are often used interchangeably in the context of quantum field theory, even though the conformal symmetry is larger.
In some particular cases it is possible to prove that scale invariance implies conformal invariance in a quantum field theory, for example in unitary compact conformal field theories in two dimensions.
Read more about this topic: Conformal Field Theory
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