Boson Fields on the Circle as Generalized Wightman Fields

We define an operator-valued distribution on the circle with the expected properties (correlation functions, Hermiticity, etc.) of the logarithmic boson field in the cylinder compact picture. This is done starting from the known Krein space realization of the right and left movers on the light cone and considering its relation with the U(1)-current algebra. The relevance of this construction fortwo-dimensional conformal quantum field theory is discussed.     

Fermion Fields,Boson Fields,and Gravitational Field

If a tetrad theory is derivable from a variational principle with a Lagrangian ?? of the form ?? = ??_F+??_M 6 tetrad components will be defined by the vacuum equations if the energy momentum tensor is symmetric. Therefore, we look for a realisation of a programme proposed in a little different way by TREDER according to which the 16 tetrad field equations should degenerate to 10 equations for the Riemannian metric if boson fields are the only source of the gravitational field.     

Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.     

Harmonic Bilocal Fields Generated by Globally Conformal Invariant Scalar Fields

The twist two contribution in the operator product expansion of for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space–time dimensions is a field V ₁ (x₁, x₂) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V ₁ can be equivalently characterized by a “single–pole property” concerning the pole structure of the (rational) correlation functions involving the product . This property is established for the dimension d = 2 of . As an application we prove that any system of GCI scalar fields of conformal dimension 2 (in four space–time dimensions) can be presented as a (possibly infinite) superposition of products of free massless fields.     

Bounded Bose Fields

Examples for bounded Bose fields in two dimensions are presented.     

Interstellar Magnetic Fields

Methods of investigating interstellar magnetic fields in spiral galaxies are reviewed. Linearly polarized radio continuum emission yields information about strength and structure of the field. Data are available for our Galaxy and several nearby galaxies. The field strengths vary between 3 and 13 , ?G; a correlation with the average surface mass density of the galaxies is indicated. The field of M31 is probably concentrated in a ring-like torus, as predicted by the dynamo theory. The field structure of M33, however, appears to be bisymmetric as expected in the primordial theory of field origin. Other candidates for a bisymmetric field structure are M51, M81, M83, NGC 2903, and NGC 6946, but the observations are not yet conclusive. The magnetic field in IC 342 is too complicated to be described in terms of a simple model. The interaction processes between the field and the various components of interstellar gas should be investigated in more detail.     

Self-Induced Electrostatic Fields

Electrostatic fields with localized sources induced by the electrostatic potential are introduced. The case in which such fields are determined by Schrödinger-like equations is considered. The problem of charge quantization is discussed.     

自对偶场与规范场相互作用理论的Faddeev－Jackiw量子化

本文采用Ｆａｄｄｅｅｖ－Ｊａｃｋｉｗ量子化方法，讨论了二维时空中一种自对偶场与规范场的相互作用理论．通过与Ｄｉｒａｃ方法的比较，建立了这两种方法的等价性