To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

https://science.sciencemag.org/content/sci/179/4079/1227.2.full.pdf

Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity. Steven Weinberg. Wiley, New York, 1972. xxx, 658 pp., illus. $18.95

Density functional. Theory and application to atoms and molecules

Space–Time Structure By Erwin Schrodinger. Pp. viii + 119. (Cambridge: At the University Press, 1950.) 12s. 6d. net.

Space-Time Structure

If the relativity principle, which states that the law of propagation for light has the same form for all macroscopic observers, is extended to include quantum observers, this leads directly to the quantum unified field theory which was introduced in a previous paper. This theory appears suitable for describing all known interactions. Gravitation and electromagnetism are described by the Einstein equations ${G}_{\ensuremath{\mu}\ensuremath{\nu}}=\frac{1}{2}({e}_{\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{-}{K}_{\ensuremath{\mu}}{j}_{\ensuremath{\nu}}\ensuremath{-}{K}_{\ensuremath{\nu}}{j}_{\ensuremath{\mu}})\ensuremath{-}R{K}_{\ensuremath{\mu}}{K}_{\ensuremath{\nu}}$, where ${G}_{\ensuremath{\mu}\ensuremath{\nu}}$ is the Einstein tensor, $R$ is the Ricci scalar, ${e}_{\ensuremath{\mu}\ensuremath{\nu}}$ is the usual stress-energy tensor for the free electromagnetic field, and ${j}_{\ensuremath{\mu}}$ is the electromagnetic current. The vector ${K}_{\ensuremath{\mu}}$ plays a dual role. It is the electromagnetic vector potential in the covariant Lorentz gauge, and, it is also a unit timelike vector interpretable as the velocity of the observer.

Quantum unified field theory from enlarged coordinate transformation group. II

A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group enlargement was accomplished by including those transformations to anholonomic coordinates under which conservation laws are covariant statements. Field equations have been obtained from a variational principle which is invariant under the larger group. These field equations imply the validity of the Einstein equations of general relativity with a stress-energy tensor that is just what one expects for the electroweak field and associated currents. In this paper, as a first step toward quantization, a consistent Hamiltonian for the theory is obtained. Some concluding remarks are given concerning the need for further development of the theory. These remarks include discussion of a possible method for extending the theory to include the strong interaction.

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Unified Field Theory From Enlarged Transformation Group. The Consistent Hamiltonian

The relativity principle that the law of propagation for light has the same form for all macroscopic observers is extended to include quantum observers; i.e., observers who may be large, but not infinitely large, by comparison with quantum mechanical systems. This leads to the extension of the covariance group from the diffeomorphisms to the conservation group (which is the largest group of coordinate transformations under which conservation laws are covariant statements) and, thus, to the quantum geometry and quantum unified field theory considered in a previous paper.

Quantum Geometry from Coordinate Transformations Relating Quantum Observers

Schrodinger considered the variational principleδ ∫$\sqrt { - g} {\text{ }}d^4 x = 0$, whereg is the determinant of the metricgμυ, but noted that ifgμυ is varied, the resultingEuler-Lagrange equations cannot serve as field equations. We writegμυ =gijhμihυj, where gij = diag(-1, 1,1, 1), and express the vectors of the tetradhμi as derivatives ofnonintegrable functions xi of the typecommonly used for phase factors in gauge theory, i.e.,hμi =x,μi. We have previously shownthat if the xi are varied, the resultingEuler–Lagrange equations serve as field equations which imply the validity of Einstein equationswith a stress-energy tensor for the electroweak fieldand associated currents. In this paper, we express theseEinstein equations into two new forms, and use these forms to derive Lorentz-force-likeequations of motion. The electroweak field appears as aconsequence of the field equations (rather than as a“compensating field” introduced to secure local gauge invariance). There is no need forsymmetry breaking to accommodate mass, because the gaugesymmetry is approximate from the outset.

Dave Pandres

Papers

Quantum unified field theory from enlarged coordinate transformation group. II

Unified Field Theory From Enlarged Transformation Group. The Consistent Hamiltonian

Quantum Geometry from Coordinate Transformations Relating Quantum Observers

Gravitational and Electroweak Interactions

Unified Field Theory from Enlarged Transformation Group. The Consistent Hamiltonian