Maximal violation of Bell's inequalities is generic in quantum field theory

Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.     

Quantum field theory and the coloring problem of graphs

The ^k theory is compared with the multilinear theory of scalar fields ₁, ₂, ..., _k having the same mass as that of . In particular, it is shown that Feynman integrals encountered in the ³ theory are not necessarily present also in the _{1 2 3} theory, but they are if they correspond to planar Feynman graphs having no tadpole part. Furthermore, a necessary and sufficient condition for the presence of a ³ Feynman integral in the _{1 2} ² theory is found. Those considerations are applications of graph theory, especially of the coloring problem of graphs, to Feynman graphs.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Adjoint solutions of the Brans-Dicke equations

It is shown that if the Brans-Dicke equations have the solution,g _ij generated by the trace free sourceT _n (T-O) then there exists an adjoint solution ^–1, ²g_ij of these equations generated by the source ^-2 T _u. An example is considered.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Further extension of the Gauss-Hertz principle

The continuum form of the Gauss-Hertz principle is extended to include the time domain as well as space. The Schrödinger equation and general relativity are derived by this method. The equivalence of the principle is shown to that of the Hamiltonian method where the energy is the expression –[ ² +A·² A], with being the difference between the acceleration potential and potential energy density, andA being the difference between the vector potentials of the acceleration field and the force field. The goal of Hertz to demonstrate a third arrangement of the principles of mechanics...which starts with... time, space and mass has apparently been achieved for relativity and for quantum mechanics, in addition to those classical equations previously found.     

General vacuum solution for Brans-Dicke-Bianchi type V

In this paper we have obtained the general vacuum solution for Bianchi type V in the Brans-Dicke theory. It is shown that for the special case=0, the sourceless scalar field is dynamically an essential factor which determines the cosmological expansion parametersR _i and the singularity does not occur whent=0. For this solution there is no antigravity (>0), which disagrees with other solutionsa for BDT-Bianchi type V     

Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this result holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form /t = W(), where is an order parameter,W is an arbitrary function of , and is a linear Hermitian operator. We speculate on the implications of this result.     

Embedding of posets into lattices in quantum logic

It has been proposed that some posets of quantum logic could be embedded into lattices in order to recover the lattice structure avoiding the introduction of ad hoc axioms. We consider here the embedding _s of any posetS into the complete lattice _s of its closed ideals (normal embedding ofS) and show that _s can be characterized (up to a lattice isomorphism) either by means of a density property or by means of a minimality property. Both of these suggest that the normal embedding satisfies some intuitive conditions which make it preferable with respect to other possible embeddings ofS. We consider the poset of all the effects associated to yes-no experiments and briefly comment on the application of the normal embedding in this case. The possibility of giving a physical interpretation to the elements of is also discussed.Research sponsored by CNR and INFN (Italy).     

Anisotropic fiber with cylindrical polar axes

The newly proposed anisotropic fiber structures with cylindrical polar principal axes appear to be an interesting novel class of special lightguides. In this paper, some interesting results relating to such fibers are derived which, to the knowledge of this author, have not yet been reported in the literature. It is found that, ifn _c0 ( )^1/2>n _zc0( _r )^1/2, TE₀₁ will be the fundament mode with a range of single-mode operation given by 2.61n _zc0 (2 _r )^1/2 /a<2.61n _c0(2 )^1/2. On the other hand, ifn _zc0 ( _r )^1/2>n _c0( )^1/2, then TM₀₁ becomes the fundamental mode whose single-mode operation range is 2.61n _c0 (2 )^1/2 /a<2.61n _zc0(2 _r )^1/2.     

A rigorous block spin approach to massless lattice theories

The renormalization group technique is used to study rigorously the ()⁴ perturbation of the massless lattice field in dimensionsd2. Asymptoticity of the perturbation expansion in powers of is established for the free energy density. This is achieved by using Kadanoff's block spin transformation successively to integrate out high momentum degrees of freedom and by applying ideas previously used by Gallavotti and Balaban in the context of the ultraviolet problems. The method works for arbitrary semibounded polynomials in and .Supported in part by the National Science Foundation under Grant No. PHY 79-16812On leave from Department of Mathematical Methods of Physics, University, PL-00-682 Warsaw, Poland     

Instantaneous Fluorescence Quantum Yield—A New Quantity with Characteristic “Fingerprints” for Excited-State Processes

The instantaneous fluorescence quantum yield _ins—a new quantity for fluorescence studies defined as the ratio of the fluorescence intensity to the optical density, both measured at the moment of the maximum of the exciting pulse—proves to be a very sensitive function for excited-state processes. Dependent on the excitation intensity _ins exhibits characteristic features (maxima/minima) indicating, for example, excited-state absorptions and annihilation processes. _ins is therefore more informative as the intensity dependence of the usually utilized fluorescence yield, the information content of which is restricted because this function is hardly structured. In the paper the influences of specific molecular parameters (excited-state absorption cross section, annihilation constant) on _ins are given, problems of the experimental accessibility of _ins are discussed, and an experimental setup for determination of this new quantity is presented. The application of the method is demonstrated for identification of excited-state absorptions of organic molecules in solution.     

The ɛ-expansion for the Hierarchical Model

In this paper, the Hierarchical Model is studied near a non-trivial fixed point of its renormalization group. Our analysis is an extension of work of Bleher and Sinai. We prove the validity of the -expansion for . We then show that the renormalization transformations around have an unstable manifold which is completely characterized by the tangent map and can be brought to normal form. We then establish relations between this result and the critical behaviour of the model in the thermodynamic limit.     

Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids

We construct a family of probability spaces,P ), <0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow _t (time evolution) leavingP globally invariant. _t is obtained as the limit of Galerkin approximations associated with Euler equations.P is also in invariant measure for a stochastic process associated with a Navier-Stokes equation with viscosity, , stochastically perturbed by a white noise force. Dedication. After completion of this work the terrible news of the sudden death of Raphael Høgh-Krohn reached us. In deep sorrow we mourn his departure. The present work has its roots in previous inspiring work by him and we dedicate it to him as a small sign of our gratitude.     

Convergence of Chorin-Marsden product formula in the half-plane

Consider a viscous incompressible fluid in the half-plane and letu _t be a solution of the Navier-Stokes equation. In this paper we prove that the product formula (E _t/n G _t/n u) ⁿ u ₀, whereE _t is the Euler flow,G _t is the heat flow and is a suitable operator describing the vorticity production due to the boundary, converges uniformly tou _t in the limitn .Research supported by Ministero della Pubblica Istruzione, CNR contract No. 84.00016.02 and GNFM     

Theory of fiber bundle with local metric of internal space and gravitation with torsion

In this paper we propose a new theory of a fiber bundle provided with a local metric of internal space. The fibers differ from usual fibers, having an enlarged factor. The enlargement may be procured by a differential mapping(x) from structure groupG to the fiberF _x atx M, and(x)R. The torsion presented stems from the local metric of internal space and the local metric stems from a induced mapping _*(x) of(x). From the theory we can get the Brans-Dicke theory with torsion. If we assume the spin density of the gauge field determines the enlarged factor of the fiberF _x, our theory is an extended Cartan theory.     

Decay of a Yang-Mills field coupled to a scalar field

Consider a gauge fieldF and a scalar field with a self-couplingV() as well as the standard coupling betweenF and . If 02V()·V(), there are no classical lumps. IfV()=||⁴ the system is conformally invariant and all the energy radiates out along the light cone.Research supported in part by NSF grants MCS 77-01340 and MCS 78-03567     

Inclusive φ meson production in neutron–carbon interactions at 20–70 GeV

mesons have been reconstructed from their decay to positive and negative kaons, using the data obtained from interaction of neutrons at 20–70 GeV with a carbon target collected by EXCHARM experiment at the Serpukhov accelerator. The analysis relies on the use of reconstructing trajectories and particle identification. From about 45 million events (19600 ± 350) mesons were found. The meson mass is measured to be (1019.4 ± 0.1)MeV/c ²; the meson width is measured to be (4.9 ± 0.3)MeV/c ². The investigation has been performed at the Joint Institute for Nuclear Research at the Laboratory of Super High Energies.     

Strings and the Gauge Theory of Spacetime Defects

We present a new topological invariant todescribe space-time defects which is closely related tothe torsion tensor in a Riemann–Cartan manifold.By virtue of the topological current theory and-mapping method, we show that there must existmultistring objects generated from the zero points ofthe -mapping. These strings are topologicallyquantized. The topological quantum numbers are thewinding numbers described by the Hopf indices and the Brouwerdegrees of the -mapping.     

Phase transformations in quaternionic quantum field theory

Phase transformations of a scalar quaternionic quantum field are examined as unitarily implemented symmetries. Under very general quantization conditions it is shown, in both global and local cases, that the only sensible phase invariance that has been suggested is pp ^–1, wherep is a quaternion and a quaternionic scalar field.