An algebraic classification of neutrino fields in general relativity

An algebraic classification of neutrino fields in curved space-times is found. Several classes are simplified by assuming a positive energy density. These classes then correspond algebraically to null and non-null electromagnetic fields. The uniqueness of the neutrino fields for these classes is discussed.     

On the spinor rank of Fermi fields

We show that any Wightman field satisfying equal-time anti-commutation relations involving space derivatives of degree at mostr must have spinor rankr + 1.     

Global spinor fields in space-time

This paper is concerned with space-time manifolds that are space- and time-oriented, causal, and possess spinor structures. Five propositions are proven: (1) If a connected, space- and time-oriented manifold is simply con-nected, then it is non-compact; (2) If such a manifold is simply connected, it admits a spinor structure, which, moreover, is unique; (3) If the space-like section of M is compact, then there exists a global system of orthonormal tetrads on M; (4) The necessary and sufficient condition for every space-time M whose space-like section is compact to admit a spinor structure is that M have a global system of orthonormal tetrads; (5) Every space-time M which can be imbedded in R⁶ admits a spinor structure. It is further suggested that in view of the fact that the existence of a spinor structure is related to homotopy properties, space-time manifolds may be classified in terms of their homotopy groups _i (M), i=1,2, 3,4. In a concluding section, some avenues for future research are discussed.Supported by the National Science Foundation.     

Cosmic spinor fields and the early universe

The energy production through expansion of the universe is studied for the Dirac spinor field in all three types of Robertson-Walker universes. Only in the open case is the matter production unlimited (closed universe: limited; flat universe: impossible). The physical properties of the cosmological solutions to the Dirac equation over any RW background are studied in detail.     

Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

Gravitational fields,spinor fields,and groups of motions

The problem of finding the most general spinor field possessing the same symmetry as a given gravitational field is solved for every group of motions. Its connection with the resolution of Einstein-Dirac equations is briefly pointed out.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Nonlocal interaction of spinor and pseudoscalar fields

The nonlocal interaction of a spinor and a pseudoscalar field is considered in the framework of gradient coupling. By the introduction of a relativistically invariant form factor in the neutrino propagator, renormalizability of the theory is achieved. It is shown that the number of primitive diagrams is just four, one of which is the neutrino self-energy diagram. The Pauli-Villars regularization procedure is carried out for this diagram.This paper was presented at the session of the Nuclear Physics Section of the USSR Academy of Sciences in Moscow (February 1–4, 1978).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 84–88, July, 1980.We are grateful to G. V. Efimov and N. Atakishiev for discussing the results.     

Scalar and spinor fields in the very early universe

Here it is shown how the vacuum energy may dominate the energy density of the very early universe even when the Higg's field in the Coleman-Weinberg potential is confined near the origin at extremely high temperature and the inflationary scenario may start. Also it is shown that supersymmetry breaking may be responsible for this phenomenon. Thus it provides another support for the hypothesis of primordial inflation proposed by Ellis et al. [4],     

Quantum gravity model with fundamental spinor fields

We discuss the possibility that gravitational potentials (metric, coframe and connection) may emerge as composite fields from more fundamental spinor constituents. We use the formalism of Poincaré gauge gravity as an appropriate theoretical scheme for the rigorous development of such an approach. We postulate the constitutive relations of an elastic Cosserat type continuum that models spacetime. These generalized Hooke and MacCullagh type laws consistently take into account the translational and Lorentz rotational deformations, respectively. The resulting theory extends the recently proposed Diakonov model. An intriguing feature of our theory is that in the lowest approximation it reproduces Heisenberg’s nonlinear spinor model.     

On the analogy between neutrino and nonlinear spinor fields

This paper considers some aspects of the neutrino dynamics i.e. connection between neutrino and nonlinear spinor fields (due to torsion).     

Conditional entropy in algebraic statistical physics

The notion of conditional entropy as entropy of conditional state on C^*-algebra with respect to its C^*-subalgebra ₁ is introduced. It is proved that for a compatible state σ on (which admits the conditional expectation of Umegaki-Takesaki) the mean conditional entropy in an a priori state σ₁ on ₁ is equal to the difference of the entropy of the state σ on and the entropy of the state σ₁ on ₁. The conditional entropy enables us to define the input-output information of a quantum communication channel in analogy to the classical Shannon formula.     

Thick brane solutions supported by two spinor fields

Stationary thick brane solutions supported by two spinor fields are considered. Two spinor fields are used here to exclude the off-diagonal components of the energy-momentum tensor of the spinor fields. The trapping of a test scalar field on the brane is also considered.     

Axial anomaly and boundary terms for general spinor fields

Index and G index for general spinor fields are evaluated by topological methods. This leads to a simple determination of the axial anomaly for general spinor fields and of the nonlocal boundary term, which allows for fractional winding numbers in spite of the integrality of the index. The results are relevant for gravitational vacuum tunnelling of higher spin fields.     

Scalar fields in a seven-dimensional manifold behaving as Lorentz-covariant spinor fields in space-time

A Lorentz-invariant model of vacuum is given in the form of a 7-dimensional manifold endowed with a statistical metrical tensor. Certain scalar fields on this manifold behave then as spinor fields when viewed from their space-time projection. This paper generalizes previous work fromSO(3)-covariance to Lorentz-covariance.     

Random walk construction of spinor fields on a three-dimensional lattice

Euclidean-invariant Klein-Gordon, Dirac and massive Chern-Simons field theories are constructed in terms of a random walk with a spin factor on a three-dimensional lattice. We exactly calculate the free energy and the correlation functions which allow us to obtain the critical diffusion constant and associated critical exponents. It is pointed out that these critical exponents do not satisfy the hyper-scaling relation but the scaling inequalities. We take the continuum limit of this theory on the basis of these analyses. We check the universality of the obtained results on other lattice structures such as the triclinic lattice and the body-centered lattice.     

On the geometric and algebraic foundation of the spinor formalism and the application to relativistic field equations

The Hilbert calculus of segments plays an important role in the axiomatic foundation of the Euclidean geometry, as the relationship to some fundamental agebraic structures can be made more apparent. An extension of the Hilbert calculus to the field of the quaternionsU2 or biquaternionsU4 leads to some new aspects on the spinor formalism. By that, a geometrical interpretation of the Dirac equation is obtained. Including the torsion of the Minkowski space (Cartan geometry), the affine connection of the spinor spaceU4 also can be interpreted with the help of a generalized Hilbert calculus. These considerations lead to a simple geometrical access to the nonlinear spinor theory, proposed by Ivanenko, Heisenberg, Dürr, etc.