Field Theory Interpretation Research Articles

The Relation between Complex Fluctuations of the Metric, the Cosmological Constant Problem and Electrodynamics in Einstein's Unified Field Theory

The interpretation of Einstein's unified field theory with sources as a gravoelectrodynamics in a polarizable continuum is considered, and the influence exerted on the background stress energy momentum content of spacetime and on the polarizability by complex fluctuations of the metric field is investigated. It is shown that certain assumptions about the fluctuating metric field which comply with the requirement of local Lorentz invariance for freely falling observers simultaneously provide a possible answer to the question of the cosmological constant and ensure that the macroscopic behaviour of weak electromagnetic inductions and fields is just the one occurring in Einstein·Maxweli electrodynamics. We do not believe that Einstein's unified field theory!) is a complete theory, capable of accounting for the behaviour of charged matter through everywhere regular solutions of its field equations. We rather hold the opinion that the tensor quantities on the left-hand sides of those equations provide definitions of properties of charged matter in terms of geometric entities, as it occurs for uncharged matter in the general relativity of 1915, and that the conservation identities express laws imposed on the properties of matter by the non-Riemannian geometric structure of the theory. We introduce a real four-dimensional manifold with coordinates Xi and write 2 ) the definitions of material properties in terms of a nonsymmetric tensor density gik and of a nonsy~metric affinity Til as follows:

Higher-level Kac-Moody string models and their phenomenological implications

We present a systematic approach to string compactifications in which some of the gauge interactions are realized at higher Kac-Moody level. This can be realized in the current constructions of four-dimensional strings including symmetric and asymmetric compactifications. It is shown that there exist higher-level models which can be obtained from exactly marginal deformations of a level-one model, and a simple field theory interpretation is provided in terms of flat scalar field directions in the original level-one model. We then consider the phenomenological possibilities opened to four-dimensional higher-level string models. In particular we show how the levels associated to standard model interactions as well as the massless content of the theory are constrained by unitarity and the renormalization group equations. We also consider the prospects for string GUT models. Mechanisms like “missing partner” in SU(5) or “see-saw” neutrino in SO(10) are only possible for k ⩾ 5. For E 6 at any level only adjoints or fundamentals can be light. A generic feature of the unification models seem to be the existence of relatively light chiral multiplets transforming like (8, 1, 0) + (1, 3, 0) + (1, 1, 0) under SU(3) × SU(2) × U(1). The problems of neutrino masses and proton stability are reconsidered and a possible simultaneous solution involving a discrete gauge symmetry is suggested.

Physical interpretation of quantum field theory in noninertial coordinate systems.

In the upper and lower quadrants of flat spacetime, (\ifmmode\pm\else\textpm\fi{}T>\ensuremath{\Vert}X\ensuremath{\Vert}) it is possible to introduce a system of coordinates in which the metric is explicitly time dependent. The conventional interpretation of quantum field theory, based on a Fock basis, cannot be implemented in a natural fashion in such coordinates. This difficulty suggests that quantum theory is covariant only for a subset of the coordinate transformations which are allowed in the classical theory.

The Induction of Electric Forces by Pressure and Energy in Einstein's Unified Field Theory with Sources

An interpretation of Einstein's unified field theory as a gravo·electrodynamics in a polarizable continuum is considered, and the influence of the matter content of the continuum on the polarizability is investigated. It is shown that, if charges at rest are embedded in a background medium endowed with uniform, isotropic stresses and with uniform energy density, Coulomb forces mediated by the electric field are produced; the stresses and the energy density of the continuum are modified by the presence of the charges, and provide the extra forces needed to keep the interacting charges in equilibrium.

Morse theory interpretation of topological quantum field theories

Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained.

Quantum group interpretation of some conformal field theories

We show that the representation theory of the q-deformation of SU(2) provides solutions to the polynomial equations of Moore and Seiberg for rational conformal field theories whenever q is a root of unity. The q-analogue of the 6 j-symbols give the duality matrices, and there is a close connection between the modular properties of the Kaĉ-Moody character for SU(2) k and some simple properties of the q-characters of quantum groups. We show how the quantum group can be considered for most purposes as a rather accurate description of the Wess-Zumino-Witten theory at level k, where k is determined by q.

Closed currents, vector fields, and phenomena

A pedagogical discussion is given of the role played by certain vector fields and closed currents in the formulation and interpretation of quantum mechanics and quantum field theory.

Objective interpretations of quantum mechanics and the possibility of a deterministic limit

Examines a suggestion by Bell (1984) that a deterministic model might be furnished by the continuum limit of an objective stochastic model which he has proposed for quantum field theory on a lattice. The virtues of models of Bell's type for general quantum systems are discussed, and it is shown that for a system of a fixed number of particles such a model does yield the deterministic de Broglie-Bohm model in an appropriate limit. It is argued, however, that a deterministic limit is unlikely to emerge from a quantum field theory capable of describing particle production and decay. An interpretation of quantum field theory is proposed which has the advantages of Bell's interpretation but is closer to conventional quantum mechanics.

An alternative to the field theory interpretation of cooperative dyadic behavior

Of major concern herein is the possibility that the purported empirical suport for Model II of field theory is supirous. Model II focuses on only the variation in behavior within dyadic sets and is empirically supported when this behavior is some function of target magnitude. It is shown, however, that other linkage mechanicms also assume the variation in behavior within dyadic sets is a function of target magnitude. Thus, it is logically possible that the empirical patterns interpreted as proof of Model II's validity actually are the product of other general models. Such a general model, which focuses on the behavior best explained by Model II, is advanced and tested using the DON data. This general model is empiricaly supported and is more attractive than Model II because it explains variation not only within dyadic sets, but also across dyadic sets. There is thus serious question as to the degree of empirical support for Model II.

On gauge invariant bosonic string quantization

It is argued that gauge invariance of the first quantized bosonic string is preserved by a mutual cancellation of the conformai and reparametrization anomalies. Implications for a geometric interpretation of second quantized string field theories are discussed in the conclusions.

Gauged BRST symmetry and the occurrence of higher cocycles in quantum field theory

The BRST symmetry of Yang-Mills theories can be gauged via the introduction of an anticommuting single gauge field. The construction of a local BRST operation follows, which allows an algebraic analysis of the BRST current algebra. This construction provides, in particular, a field theory interpretation of most higher cocycles which accompany the usual chiral anomaly.

Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

The center-of-mass bag model and the Lorentz-Boost

A center-of-mass (CM) bag model and its cavity approximation are suggested by introducing a phenomenological four-potential of confinement and the CM four-vector. This model, equivalent to the MIT version on the rest CM-frame, seems to provide a field-theory interpretation of our previous assumptions about the collective motion of bagged quarks and can be readily quantized.

De Sitter and conformal field theories

After a brief review of conformal gravity and conformal anomalies in field theories, this paper deals with elementary particles and quantum field theories in 3 + 2 de Sitter space and in conformal space. The importance of working in realistic space-time rather than Euclidean or spherical models, is demonstrated. The “parton-like” representations Di and Rac give rise to gauge theories of scalar and spinor fields, and a theory of interacting massless particles with all spins. This theory (in 4-dimensional de Sitter space) is constructed on the basis cf a conformally invariant field theory in 3-dimensional space-time. Conformally invariant field theories in 3 and 4 dimensional are reviewed and examined, and new proposals are made for the interpretation of massless field theories in general.

Flavouring the Gribov process

The exchange of flavour carrying trajectories is studied in the non-covariant parton interpretation of reggeon field theory. While pomeron exchange is described by wee partondensities, i.e. diagonal elements of the density matrix of a fast hadron, meson exchange is described by density matrix elements which are diagonal in parton number but off-diagonal in flavour. The reggeon field theory “hamiltonian” describes a markoffian evolution of this block-diagonal density matrix during a boost. This interpretation is possible both if there are two distinctf and ℙ trajectories and in case of ℙ identity. The meson trajectories are superpositions of odd and even signature trajectories.

Remarks on positive frequency and hamiltonians in expanding universes

We examine critically the persistent belief that the physical interpretation of a quantum field theory in curved space-time is to be found by introducing a notion of particles at each time in terms of the exact eigenstates of some energylike operator at that time. It seems that all straightforward implementations of this principle suffer from either ambiguity or failure to produce finite particle densities and renormalizable energy-momentum tensors. Calculations are done for a cosmological model of Bianchi type I, containing a scalar fieldφ whose equation includes the term ξRφ. Diagonalization of thetotal energy suggests a certain particle definition, which, however, yields a finite particle creation rate only when ξ=1/6 and the universe is isotropic. Diagonalization of acanonical Hamiltonian is a prescription loose enough to be made consistent with almost any ansatz (including one that does yield physically acceptable expectation values), hence of no theoretical value. An apparently successful naive approach to the isotropic case (for any ξ) is explained as an unconscious first approximation to an adiabatic analysis of the notion of positive frequency.

Reggeon field with non-vanishing vacuum expectation value

It is argued that if the vacuum expectation value of the reggeon field does not vanish, the solution of the reggeon calculus corresponds to the leading singularity of intercept one. The physical interpretation of the reggeon field theory with unstable vacuum is discussed.

Feynman quantization and the S matrix for spin particles in Riemannian spacetime

The Feynman space-time interpretation of quantum field theory is extended to the case of general Riemann space-time (external gravitational field). The expression in the form of a functional integral for the causal propagator is deduced by means of the proper time method and a correspondingly generalized path integral method. The interpretation of the Feynman diagrams in terms of particles and antiparticles is done in such a way that the usual space --time properties of the causal propagator (the forward movement in time of particles and backward movement in time of antiparticles) take place. The expression for the amplitude of the creation of the pair in the external gravitational field, including the instability and degeneration of the vacuum, is deduced. It is shown that vacuum instability is absent at least for closed 3-dimensional space. (auth)

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino‐Feldern Gedanken zu einer Theorie der solaren Neutrinos

AbstractThe strange non‐evidence of the solar‐neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI‐interaction constant and according to the hypotheses of PAULI, DE BROGLIE, and JORDAN the RIEMANN‐EINSTEIN gravitational metric gik is fusioned by the four independent WEYLian neutrino fields (β‐neutrinos and β‐antineutrinos, μ‐neutrinos and μ‐antineutrinos). This fusion gives four reference tetrads hiA(xl) as neutrino‐current vectors, firstly. Then, the metric gik is defined by the equation gik = ηAB hiAhηB according to EINSTEIN's theory of tele‐parallelism in RIEMANNian space‐times.The relation of the gravitation field theory to FERMI's theory of weak interactions becomes evident in our reference‐tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential hiA with the matter Tιi is given by a potential‐like (FERMI‐like) interaction term. In this interaction term two WEYL spinor‐fields are operating on the matter‐tensor, simultanously. Therefore, the gravitation coupling constant is PAULI's square of the FERMI‐constant.Besides of the fusion of the RIEMANN‐EINSTEIN metric gik by four WEYL spinors we are able to construct a conformal flat metric ĝik = ϕ2ηik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN's hermitian field theory as a unified field‐theory of the gravitational metric gik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference‐tetrads theory is resulting that the WEYL spinors in the “new metric” ĝik are interacting with the DIRAC matter current by a FERMI‐like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long‐range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long‐range interaction which is 1018 times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform‐flat this long‐range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN‐like redshift of its frequences.The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.)This radius â is 1018 times larger than the EINSTEIN‐SCHWARZSCHILD gravitation radius a = fM/c2: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self‐absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long‐range weak interaction potential ĝik = ϕ2ηik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions.Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN's hermitian field theory and secondly based on our reference‐tetrads theory of gravitation.

On Treder's Interpretation of Einstein's Unified Field Theory

Einstein's Unified Theory1>-a> seems to be a very natural and plausible generaliza­ tion of the General Theory of Relativity. As compared to the latter, it has six new degrees of freedom which may be associated with the electromagnetic field. Indeed, if the antisymmetric 'part of the metric g,k is connected with the dual of the field tensor ftk