Field Theory Of Elementary Particles Research Articles

Solution of a linearized model of Heisenberg’s fundamental equation II

We propose to look at (a simplified version of) Heisenberg’s fundamental field equation [see Heisenberg, W., Introduction to the Unified Field Theory of Elementary Particles (Wiley, New York, 1966)] as a relativistic quantum field theory with a fundamental length, as introduced by Brüning and Nagamachi [J. Math. Phys. 45, 2199 (2004)], and give a solution in terms of Wick power series of free fields which converge in the sense of ultrahyperfunctions but not in the sense of distributions. The solution of this model has been prepared by Nagamachi and Brüning [arXiv:0804.1663] by calculating all n-point functions by using path integral quantization. The functional representation derived in this part is essential for the verification of our condition of extended causality. The verification of the remaining defining conditions of a relativistic quantum field theory is much simpler through the use of Wick power series. Accordingly in this second part, we use Wick power series techniques to define our basic fields and derive their properties.

Spontaneous skyrmion ground states in magnetic metals

Since the 1950s, Heisenberg and others have addressed the problem of how to explain the appearance of countable particles in continuous fields. Stable localized field configurations were searched for an ingredient for a general field theory of elementary particles, but the majority of nonlinear field models were unable to predict them. As an exception, Skyrme succeeded in describing nuclear particles as localized states, so-called 'skyrmions'. Skyrmions are a characteristic of nonlinear continuum models ranging from microscopic to cosmological scales. Skyrmionic states have been found under non-equilibrium conditions, or when stabilized by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids, spin textures in quantum Hall magnets, or the blue phases in liquid crystals. However, it has generally been assumed that skyrmions cannot form spontaneous ground states, such as ferromagnetic or antiferromagnetic order, in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed-matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model based on a few material-specific parameters that can be determined experimentally. Our model has a condition not considered before: we allow for softened amplitude variations of the magnetization, characteristic of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist generally in a large number of materials, notably at surfaces and in thin films, as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.

Numerical simulations in quantum field theory of elementary particles

Quantum field theory of particles like electrons or quarks, which are the elementary constituents of matter, describes the interactions between these particles, in particular their frequent transmutations due to quantum fluctuations. Many experimental data on the structure of matter (e.g., of proton), and its properties observed by means of the high energy particle accelerators, can be explained by such a theory. In many cases massive numerical simulations of this theory formulated on a finite space-time lattice are required, however. We explain the basic physical principles of the lattice formulation of quantum field theory and its mathematical realization. For finite values of the lattice spacing and finite volumes, the theory can be simulated numerically by means of the Monte Carlo methods. The process of approaching the continuous space-time, using the statistical theory of critical phenomena, is understood in principle, but it requires immense computational resources and elaborate algorithms. We introduce some of these algorithms and give examples of current achievements like an explanation of the confinement of quarks, the fact that quarks cannot be observed experimentally as individual free particles.

The barut and zanghi model, and some generalizations

In this paper we give a detailed analysis of the Barut and Zanghi (BZ) model, which can be seen as a classical model for a Dirac particle. We show that all helical worldlines in the BZ model have vanishing third curvature. We also study some generalizations of the BZ model. There is a particularly interesting one, considered in detail, which can be seen as a classical model for Heisenberg program of a unified field theory of elementary particles.

Cosmological constant as integration constant

AbstractEinstein's field theory of elementary particles (Einstein 1919) yields black holes with a mass M ˜ G−1 Λ−1/2c2 and a charge Q ˜ G−1/2λ−1/2c2, their curvatu re radius is Λ−1/2. Here 4Λ is an integration constant of Einstein's ‘trace‐less’ gravitation equations.The choice λ = G−1h−1c3 for this constant defines Planckions and implies “strong gravity”. The choice λ = λ = 3Hinf2c−2 (where Hinf means the Hubble parameter of a final de Sitter cosmos) involves “weak gravity” and describes an electro‐vac spherical universe.

A nonlinear gauge-invariant field theory of elementary particles

The field theory of Cooperstock and Rosen (Int. J. Theor. Phys. 28, 423 (1989)), which modelled leptons, is enlarged to encompass the two known quark families. The singularity-free field theory constructs the particles in solitonlike structures via the nonlinear interaction of three scalar fields and the electromagnetic field. The theory predicts particle sizes that are consistent with experiment.

The Second Creation: Makers of the Revolution in 20th‐Century Physics

Probably the most remarkable aspect of 20th century physics is that it has made possible the rational investigation of the ultimate structure of matter and the origin of the universe. When a number of prominent physicists before the turn of the century thought that fundamental physics was essentially over, their conception of the scope of the field hardly included the structure of ordinary matter, much less the exotic forms dealt with routinely today. The often halting progress through this century in understanding the nature of matter was punctuated by three periods of synthesis. The first of these produced the quantum mechanical theory of atomic structure, the second successfully merged this theory with special relativity to form quantum electrodynamics, and the third resulted in the “standard” gage quantum field theory of elementary particles.

Gravitation und bilokale Feldtheorie / Gravitation and Bilocal Field Theory

Abstract Gravitation and Bilocal Field Theory The starting point is the conjecture that a field theory of elementary particles can be constructed only in a bilocal version. Thus the 4-dimensional space time has to be replaced by the 8-dimensional manifold of all ordered pairs of space time events. With special reference to the Schwarzschild metric it is shown that the embedding of the space time into the manifold yields a description of the gravitational field.

The unified field theory of elementary particles: Some recent advances

Progress in the unified field theory of elementary particles over the last seven years includes experimental verification of the scale group and its application in theoretical investigations; connecting the unified field theory with phenomenological current algebra; exploring the consequences of the indefinite metric for the problem of causality and the classification of leptons; elaboration of methods for the calculation of mass eigenvalues; and experimental verification of the predicted behavior of cross-sections at extremely high energies.

Example of a covariant field theory of elementary particles

Example of a covariant field theory of elementary particles

Review Lecture. Calculations of nuclear structure

The field theory of elementary particles has so far failed to predict the detailed form of the interaction between neutrons and protons (nucleons), but the nucleon-nucleon scattering experiments are now sufficiently complete that for most purposes the interaction may be taken as known. At the same time a wealth of data concerning energy levels, transition probabilities and so on is available for literally hundreds of nuclei. Such measurements reveal that nuclei have an extremely rich structure, with both single-particle and collective properties, illustrating almost every feature of a many-body system. It is the purpose of this talk to review the extent to which we are able to understand these properties on the basis of the known two-body interaction. It will be shown how some features may be understood quite readily while others still pose fascinating problems.

Unified field theory of elementary particles

Unified field theory of elementary particles

The goldstone theorem photons and sommerfeld’s fine-structure constant

The notion of spontaneous breakdown of isospin symmetry as the origin of the photon is investigated in the framework of the unified field theory of elementary particles on the basis of the Goldstone theorem. The treatment evolves towards a particularity of quantum electrodynamics in the hierarchy of interactions. Progress with regard to the problem of unwanted zerons is also reported. An attempt is made to clarify the physical basis of the successes of the unified theory of elementary particles.

Unified field theory of elementary particles

Unified field theory of elementary particles

Unified field theory of elementary particles

Unified field theory of elementary particles

Introduction to the Unified Field Theory of Elementary Particles

<i>Introduction to the Unified Field Theory of Elementary Particles</i>

Two ways of spontaneous symmetry breaking

A distinction between two types of spontaneous sym metry breakings is made: “asymptotical” breaking and “local” breaking. The former is characterized by a conserved symmetry current and by the presence of Goldstone bosons (or long-range interactions), and occurs in the BCS-theory as well as in classical theories. For local breakings the usual proof of current conservation breaks down as a result of the singularity of a product of field operators at one point, as occurring in currents and their divergences. This case is realized in certain local quantum field theories,e.g. in quantum electrodynamics with zero bare mass. Local breakings, in contradistinction to asymptotical ones, might be useful in a field theory of elementary particles.

Heisenberg Field Theory

Introduction to the Unified Field Theory of Elementary Particles By W. Heisenberg. Pp. ix + 177. (London and New York: Interscience Publishers, a Division of John Wiley and Sons, 1966.) 47s.

Isospin und Parität in der nichtlinearen Spinortheorie

The isospin transformation properties and the space reflection symmetry in a nonlinear field theory of elementary particles, as proposed by HEISENBERG and coworkers, are studied. In section I it is shown that the nonlinear equation for a 4-component spinor operator ψ is equivalent to the equation for a 4-component WEYL- isospinor operator χ. In this WEYL representation of the theory the PAULI-GÜRSEY transformations and the TOUSCHEK transformation can be replaced by the conventional forms of the isospin rotations and the gauge transformation of the first kind, respectively. In section II an attempt is made to introduce parity in a rigorous manner using the invariance of the equation under l-Inversion l→ —l. Some important aspects of symmetry operations which involve transformations of parameters, are discussed. By virtue of the parity symmetry a DIRAC notation may be introduced, and the nonlinear equation then corresponds to a TOUSCHEK invariant equation of the DIRAC type with nonlinear vector- and axialvector terms of equal strength. The existence of particles with finite mass suggests a degeneracy of the ground state “world” with respect to parity. In section III and IV the TAMM—DANcoFF-method is applied for an estimate of the masses of nucleons and bosons with spin and isospin zero or one, using the simpler WEYL representation with and without consideration of the parity symmetry, respectively.

Calculations on Classical Field Theory

The equations of the classical field theory of elementary particles proposed by one of the authors were integrated numerically for the static, spherically-symmetric case. A solution was obtained corresponding essentially to minimum energy, and hence describing a classical electron according to the theory. It was found that the frequency associated with the solution was zero, to within the accuracy of the calculations, for the case of minimum energy. Hence the theory, in its present form, is not capable of accounting for the Sommerfeld fine-structure constant, as had seemed possible.