A complete set of Lorentz-invariant wave packets and modified uncertainty relation

Abstract

We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly Lorentz-invariant completeness relation (resolution of identity). The position-momentum uncertainty relation for this Lorentz-invariant wave packet deviates from the ordinary Heisenberg uncertainty principle, and reduces to it in the non-relativistic limit.

Comments: 44 pages, references added, more explanations given, version accepted for publication in Eur. Phys. J. C (v3); a typo in Eq.(160) is corrected (v4)