Article

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,

“…Therefore the theory is not mathematically consistent. This confirms the results of previous research [3] [4].…”

Section: Discussionsupporting

confidence: 93%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

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

2007

Phys. Scr.

“…This problem was also discussed in [11] where it was shown that this is due to the fact that the quantity do this is presented in [4], [5], and [11]. It is shown, for example, in [4] how equivalence between hole theory and QFT is restored by properly redefining the QFT vacuum state in the case of a time independent perturbation.…”

Section: Anomalies In Qftmentioning

confidence: 98%

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.

“…By the methods of standard time independent perturbation theory (see ref [4] and [5]) the change in the energy of a state 'n' is given by, (9) where ( ) 3 O V means terms to the third order in V or higher. The first order term ( ) 1 n ∆ε is, (10) ( ) 1 n n V ∆ε = , n and the second order term ( ) 2 n ∆ε is,…”

Section: Introductionmentioning

confidence: 99%

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

2003

Can. J. Phys.

Self Cite

Dirac's hole theory and quantum field theory are generally considered to be equivalent to each other. However, it has recently been shown that this is not necessarily the case. In this article we will discuss the reason for this lack of equivalence and suggest a possible solution.Comment: Correction to title and other minor changes to reflect the version to be published in the Canadian Journal of Physic