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Dan Solomon

Publications and source records attributed to Dan Solomon.

52 records · Page 3Linked to original sources
arXiv2005

Is formal QED mathematically consistent?

The formal structure of quantum electrodynamics consists of various elements. These include the Schroedinger equation which evolves the system forward in time, the vacuum state which is assumed to be the state with a free field energy of zero, and the principle of gauge invariance. In this paper we will examine the mathematical consistency of these elements. It will be shown that these elements, which are basic to the formal structure of the theory, are not mathematically consistent.

physics.gen-ph↗
arXiv2005

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

Diracs 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.

quant-ph↗
arXiv2004

The Heisenberg versus the Schrodinger picture in quantum field theory

The Heisenberg picture and Schrodinger picture are supposed to be equivalent representations of quantum mechanics. However this idea has been challenged by P.A.M. Dirac. Also, it has been recently shown by A. J. Faria et al that this is not necessarily the case. In this article a simple problem will be worked out in quantum field theory in which the Heisenberg picture and Schrodinger picture give different results.

quant-ph↗
arXiv2004

The stability of the QED vacuum in the temporal gauge

The stability of the vacuum for QED in the temporal gauge will be examined. It is generally assumed that the vacuum state is the quantum state with the lowest energy. However, it will be shown that this is not the case for a system consisting of a fermion field coupled to a quantized electromagnetic field in the temporal gauge. It will be shown that for this situation there exist quantum states with less energy than the vacuum state.

hep-th↗
arXiv2004

The difference between Dirac's hole theory and quantum field theory

Dirac's hole theory and quantum field theory are generally thought to be equivalent. In fact field theory can be derived from hole theory through the process of second quantization. However, it can be shown that problems worked in both theories yield different results. The reason for the difference between the two theories will be examined and the effect the this difference has on the way calculations are done in quantum theory will be examined.

hep-th↗
arXiv2003

Dirac's hole theory versus field theory for a time dependent perturbation

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 that for a time independent perturbation different results are obtained when the change in the vacuum energy is calculated. Here we shall extend this discussion to include a time dependent perturbation. It will be shown that HT and QFT yield different results for the change in the vacuum energy due to a time dependent perturbation.

quant-ph↗
arXiv2003

A problem with the Schwinger term in Dirac field theory

In order for Dirac theory to be gauge invariant it can be shown that the Schwinger term must be zero. However, it can also be shown that for the vacuum state to be the lowest energy state the Schwinger term must be nonzero. Therefore there is an inconsistency in Dirac theory involving the evaluation of the Schwinger term. This inconsistency is discussed along with a possible way to resolve it.

hep-th↗
arXiv2003

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

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.

quant-ph↗
arXiv2003

The problem of gauge invariance in Dirac field theory

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.

quant-ph↗
arXiv2002

No limit on the energy extracted from a Dirac quantum state

When a Dirac quantum state interacts with an applied electric field the energy of the quantum state changes. It is generally assumed that there is a maximum limit on the amount of energy that can be extracted from a Dirac quantum state, due to its interaction with an electric field. In this article it is shown that this assumption is not correct and that, for a properly applied electric field, an arbitrarily large amount of energy can be extracted from the quantum state.

quant-ph↗
arXiv2002

Gauge invariance and the Dirac free field energy

Dirac field theory is assumed to be gauge invariant. However it is well known that a calculation of the polarization tensor yields a non-gauge invariant result. The reason for this has been shown to be due to the fact that for Dirac theory to be gauge invariant there must be no lower bound to the free field energy. Here an additional proof will be presented to show that this is, indeed, the case.

quant-ph↗
arXiv1999

Negative energy density for a Dirac-Maxwell field

It is well known that there can be negative energy densities in quantum field theory. Most of the work done in this area has involved free non-interacting systems. In this paper we show how a quantum state with negative energy density can be formulated for a Dirac field interacting with an Electromagnetic field. It will be shown that, for this case, there exist quantum states whose average energy density over an arbitrary volume is a negative number with an arbitrarily large magnitude.

gr-qc↗
arXiv1999

Quantum states with a space-like energy momentum

A common assumption in quantum field theory is that the energy-momentum 4-vector of any quantum state must be timelike. It will be proven that this is not the case for a Dirac-Maxwell field. In this case quantum states can be shown to exist whose energy-momentum is spacelike. This implies that there must exist quantum states with less energy than the vacuum state.

hep-th↗
arXiv1999

Gauge invariance and the vacuum state

Quantum field theory is assumed to be gauge invariant. It is shown that for a Dirac field the assumption of gauge invariance impacts on the way the vacuum state is defined. It is shown that the conventional definition of the vacuum state must be modified to take into account the requirements of gauge invariance.

quant-ph↗
arXiv1999

Mathematical Inconsistencies in Dirac Field Theory

If a mathematical theory contains incompatible postulates then it is likely that the theory will produce theorems or results that are contradictory. It will be shown that this is the case with Dirac field theory. An example of such a contradiction is the problem asociated with evaluating the Schwinger term. It is generally known that different ways of evaluating this quantity yield different results. It will be shown that the reason for this is that Dirac field theory is mathematically inconsistent, i.e., it contains incompatible assumptions or postulates. The generally accepted definition of the vacuum state must be modified in order to create a consistent theory.

quant-ph↗