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Non-commutative geometry in massless and massive particles. (English) Zbl 1195.83017

Summary: We study the symmetries of massless and massive particles action. By considering the non-commutative space-time, we find appropriate non-commutative relation for relativistic particles which leaves invariant the non-commutative Minkowski space-time. We show that non-commutativity break the scale and conformal invariance in massless and massive action. So, in non-commutative space-time the massless and massive particles have same symmetry.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
83C65 Methods of noncommutative geometry in general relativity
81R60 Noncommutative geometry in quantum theory
83A05 Special relativity
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