Unified Field Theoretical Models from Generalized Affine Geometries II

The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288–1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗O ₃∼R⊗SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.     

Moderate Deviations for Random Field Curie-Weiss Models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization S _n , which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number m, a positive real number ??, and a positive integer k such that (S _n ?nm)/n ^?? satisfies a moderate deviations principle with speed n ^1?2k(1???) and rate function ??x ^2k /(2k)!, where 1?1/(2(2k?1))<??<1.     

Phase Transition and Level-Set Percolation for the Gaussian Free Field

We consider level-set percolation for the Gaussian free field on ${\mathbb{Z}^{d}}$ , d ≥ 3, and prove that, as h varies, there is a non-trivial percolation phase transition of the excursion set above level h for all dimensions d ≥ 3. So far, it was known that the corresponding critical level h _*(d) satisfies h _*(d) ≥ 0 for all d ≥ 3 and that h _*(3) is finite, see Bricmont et al. (J Stat Phys 48(5/6):1249–1268, 1987). We prove here that h _*(d) is finite for all d ≥ 3. In fact, we introduce a second critical parameter h _** ≥ h _*, show that h _**(d) is finite for all d ≥ 3, and that the connectivity function of the excursion set above level h has stretched exponential decay for all h > h _**. Finally, we prove that h _* is strictly positive in high dimension. It remains open whether h _* and h _** actually coincide and whether h _* > 0 for all d ≥ 3.     

Quantum Inequality Bounds for Free Rarita-Schwinger Field in Flat Spacetime

Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time. Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.     

Quantum Inequality Bounds for Free Rarita-Schwinger Field in Flat Spacetime

Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality (QEI), in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time.Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.     

Ising Field Theory in a Magnetic Field: Analytic Properties of the Free Energy

We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain TT _c , H0. The analysis is based on numerical data obtained through the Truncated Free Fermion Space Approach. We determine the discontinuities across the Yang–Lee and Langer branch cuts. We confirm the standard analyticity assumptions and propose extended analyticity; roughly speaking, the latter states that the Yang–Lee branching point is the nearest singularity under Langer's branch cut. We support the extended analyticity by evaluating numerically the associated extended dispersion relation.     

Strict Convexity of the Free Energy for a Class of Non-Convex Gradient Models

We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. We show using a one-step multiple scale analysis the strict convexity of the surface tension at high temperature. This is an extension of Funaki and Spohn’s result [8], where the strict convexity of potential was crucial in their proof. Supported by the DFG-Forschergruppe 718 ‘Analysis and stochastics in complex physical systems’.     

The Large Field Renormalization Operation for Classical N-Vector Models

A renormalization operation of the large field densities for the classical $N$-vector models is constructed in this paper. It allows to improve bounds of these densities, and thus to prove all inductive hypotheses. This completes the construction and analysis of the full renormalization group flow for these models. The results will be used in the next paper to analyze the correlation functions. Received: 2 February 1998 / Accepted: 12 February 1998     

Central Limit Theorem for the Free Energy of the Random Field Ising Model

A central limit theorem is proved for the free energy of the random field Ising model with all plus or all minus boundary condition, at any temperature (including zero temperature) and any dimension. This solves a problem posed by Wehr and Aizenman (J Stat Phys 60:287–306, 1990). The proof uses a variant of Stein’s method.

     

Wick-Ordered Entire Functions of the Indefinite Metric Free Field

We present a simple and general method for constructing Wick-ordered entire functions of free fields with an indefinite metric, based on using an appropriate generalization of the Paley–Wiener–Schwartz theorem.     

Topological Conformal Field Theories from the Noncompact Coset Models

It is shown in this letter that in the bosonic coset models G_kl×G_k2/G_kl+_k2 associated with noncompact Kac-Moody algebra there exist two kinds of topological points, _k2=0 and _kl+_k2-2g = 0. At these points, the coset models may be interpreted as twisted versions of noncompact counterparts of the Kazama-Suzuki models.     

在自由空间里的运动磁场和时变磁场都没有产生电场

在自由空间里,磁场运动时没有产生电场、时变磁场的辐射运动也没有产生电场.故,“磁生电”的真实原因是：金属电子在广义洛伦兹磁力的作用下的流动而形成Ic,却不是法拉第-麦克斯韦-爱因斯坦在自由空间里虚构的位移电流Id.基于唯物主义自然观,联系电磁感应的物质是洛伦兹的金属电子,却不是法拉第-麦克斯韦-爱因斯坦的真空以太.     

Mass Transfer in Free Convection Developing in a Magnetic Field

The interaction of a charged hydrated particle with an external magnetic field is analyzed under conditions of diffusion and convective mass transfer. A model of forming local space charge regions in the bulk of a solution is suggested. The model is used to study the feasibility of changing the velocity and redistribution of charged particles in an aqueous medium. The results of theoretical calculations are tested experimentally by quantitative estimation of the rate of the convective liquid flow developed in crossed electric and magnetic fields.     

The Average Free Energy and the Effective Mean Field Hypothesis

In this paper, an improvement in the variational-cumulant expansion method is made. For any model in lattice field theories, the average free energy can be calculated rigorously according to the generalized cumulant expansion, and the intensity of the effective external field can be determined by the effective mean field hypothesis. As a test, the king model is studied, and the results take a visible turn for the better.     

Are LCAO-MO Models Useful Estimators for Electric Field Gradients in Simple Molecules?

In this tutorial paper we compare the ab-initio calculations of electronic charge densities and related electric field gradients in simple molecules like H₂ as well as the triangular H₃ with variable bond distance and bond angle using the Amsterdam Density Functional (ADF) code with calculations based on a simple linear combination of hydrogen 1s-orbitals. In order to gain more insight into ADF – or other ab-initio – calculations it is rather useful to vary structural parameters. In addition to geometry optimisations we propose to vary bond distances and bond angles over extended ranges in order to arrive at a better interpretation of the results.     

The Thermodynamic Limit in Mean Field Spin Glass Models

 We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N ₁ and N ₂ sites, respectively, with N ₁ +N ₂ =N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site. Received: 19 April 2002 / Accepted: 22 April 2002 Published online: 6 August 2002