Regular Article - Theoretical Physics
A complete set of Lorentz-invariant wave packets and modified uncertainty relation
Department of Mathematics, Tokyo Woman’s Christian University, 167-8585, Tokyo, Japan
2 Department of Physics, University of Tokyo, 113-0033, Tokyo, Japan
Accepted: 24 July 2021
Published online: 20 August 2021
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.
© The Author(s) 2021
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