Some remarks on Dirac's hole theory versus quantum field theory

2006

Phys. Scr.

Section: Introductionmentioning

confidence: 99%

“…This author (Solomon [4]) found that this problem was related to the way the vacuum state was defined in QFT. If the definition of the vacuum state was modified as described in [4] then the HT and QFT would yield identical results.…”

Section: Introductionmentioning

confidence: 99%

Some new results concerning the vacuum in Dirac's hole theory

2006

Phys. Scr.

“…They concluded that the difference between HT and QFT was related to the validity of Coutino et al show that this is not necessarily the case for HT when applied to an actual problem. This author (Solomon [4]) found that this problem was related to the way the vacuum state was defined in QFT. If the definition of the vacuum state was modified as described in [4] then the HT and QFT would yield identical results.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the previous work [1][2][3][4] examined the difference between HT and QFT for a time independent change in the electric potential. In this article the differences between HT and QFT for a time dependent change in the electric potential will be examined.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some differences between Dirac's hole theory and quantum field theory

2005

Can. J. Phys.

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered to be equivalent to each other. However, it has been recently shown by several researchers that this is not necessarily the case. When the change in the vacuum energy was calculated for a time independent perturbation HT and QFT yielded different results. In this paper we extend this discussion to include a time dependent perturbation for which the exact solution to the Dirac equation is known. It will be shown that for this case, also, HT and QFT yield different results. In addition, there will be some discussion of the problem of anomalies in QFT.

A new look at the problem of gauge invariance in quantum field theory

2007

Phys. Scr.

It is generally assumed that quantum field theory is gauge invariant. However it is well known that non-gauge invariant terms appear in various calculations. This problem was examined in Refs. [3] and [4] and it was shown that at the formal level quantum field theory in the Schrödinger picture is not, in fact, gauge invariant. It was determined that this problem was due to a mathematical inconsistency relating to the way the vacuum state is defined. In order to shed further light on this problem we consider a "simple" field theory in 1-1D space-time consisting of a quantized fermion field with zero mass in the presence of a classical electromagnetic potential. It can easily be shown that for this situation the equations of motion can be solved exactly in both the Heisenberg and Schrödinger pictures. This allows us to easily identify the source of the mathematical inconsistency.induced in the vacuum state due to the application of the electromagnetic field is calledUsing perturbation theory the lowest order term of the vacuum current can be shown to be given by,