On the Impossibility of a Poincare-invariant Vacuum State with Unit Norm
Abstract
In the standard construction of Quantum Field Theory, a vacuum state is required. The vacuum is a vector in a separable, infinite-dimensional Hilbert space often referred to as Fock space. By definition the vacuum wavestate depends on nothing and must be translationally invariant. We show that any such translationally-invariant vector must have a norm that is either divergent or equal to zero. It is impossible for any state to be both everywhere translationally invariant and also have a norm of one. The axioms of QFT cannot be made internally consistent.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2008
- DOI:
- 10.48550/arXiv.0802.0216
- arXiv:
- arXiv:0802.0216
- Bibcode:
- 2008arXiv0802.0216B
- Keywords:
-
- Physics - General Physics;
- 12E25;
- 28Cxx
- E-Print:
- 6 pages