On the structure of open–closed topological field theory in two dimensions

I discuss the general formalism of two-dimensional topological field theories defined on open–closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying ‘boundary conditions’. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss reducibility of boundary extensions.     

Energy of electrons on a two-dimensional lattice in a magnetic field: perturbation theory versus “Peierls substitution”

Energy levels and total energy of electrons in a magnetic field moving in a two dimensional periodic potential are obtained. Two limiting cases are treated: the tight binding limit and the weak potential. In these cases different direct perturbation theories are applicable. The energy difference with and without magnetic field is compared with calculations based on the Peierls substitution. The latter is shown to lead to severe qualitative and quantitative errors. The sources of these errors are clarified. The spontaneous generation of a magnetic field is shown to be impossible.     

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in _kBTc/J−D/J$k_B{T}_c/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J$D/J$ and △/J$△/J$ on the phase diagrams of the system. The system exhibits clear distinctions in a qualitative manner with coordination number q$q$ for random crystal fields with △/J,D/J≠0$△/J,D/J\ne 0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.     

Regularization,renormalization and “peratization” in effective field theory for two nucleons

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, the renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff \( \Lambda\) as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit \( \Lambda\) \( \rightarrow\) ∞ yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.     

On the “covariantized light-cone” string field theory II

We present a full non-linear BRS transformation which corresponds to one of the generators of the OSp(1, 1|2) or OSp(26, 2|2) algebra using the covariantly extended joining-splitting type interaction vertex functions in open string field theory.     

Momentum space of constant curvature and the “rainbow” approximation in quantum field theory

The behavior of the mass operator is studied in “rainbow” graph approximation in the momentum space of constant curvature with the group of motions SO(4,1). The infrared divergences occuring there are eliminated by a multiplicative renormalization. When x?4ι ^?2 (whereι is the “fundamental length”), the resulting asymptotic (x ? m² _c) expressions for the mass operator Σ_R (x) and its imaginary part are analytic in the coupling constant at zero, while in the domain x?4ι ^?2 a logarithmic branching occurs, and the function grows linearly. The assumption that there are “superheavy particles” in nature (with m _c ² ?hι ^?2) in the asymptotic domain x?4ι _?2 leads to a violation of the positive definiteness for the imaginary part of the mass operator.     

“Haunted” measurements in quantum theory

Sometimes it is possible in quantum theory for a system to interact with another system in such a way that the information contained in the wave function becomes very scrambled and apparently incoherent. We produce an example which is exactly calculable, in which a macroscopic change is induced in the environment, and all phase information for the system is apparently lost, so that a measurement has seemingly been made. But actually, although the wave function has been badly scrambled, all the original information is still present. We call this situation one of latent order.Subsequently, the system interacts again with the environment, wiping out the macroscopic change, and the wave function once again becomes manifestly coherent. Thus the apparent measurement has been undone, and leaves no aftereffect. Thus, our measurement has disappeared without a trace. We call such a measurement a haunted measurement, and we believe that until the measurement process is rigorously understood, the concept of measurement is ambiguous. It is just not good enough to say that an amplification stage occurs somewhere in the process.We also point out the connection between the haunted measurement and delayed-choice experiments and discuss a haunted version of the Schrödinger's Cat experiment and of the Einstein-Podolsky-Rosen experiment.     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

Comment on: “Lorentz violation in high-energy ions” by Santosh Devasia

We analyze a recent letter submitted by S. Devasia to EPJ C.     

Indirect magnetic interaction in the “net fractal” systems

A localized spin system of fractal symmetry with indirect exchange between them is considered. We define a specific class of fractals as the “net fractals” which display multidimensional logarithmic periodicity. Basing on this property we model the effective indirect exchange interaction by the conventional RKKY exchange with the logarithmic coordinates playing role of the real space ones. Finally, we discuss the case of non-ideal “net fractals” in which fractional dynamics of the electrons is expected. In this case we show that RKKY exchange integrals are given by the formulas derived under assumption that a system has a fractional spectral dimension.     

Influence of nonlinear noncoherent particle oscillations on the transverse dimensions of an electron-ion ring in the development of instability of “serpent” type

One of the main obstacles to the formation of high-intensity electron-ion rings for the collective method of acceleration is transverse two-beam instability of serpent type, the existence of which is associated with the presence of coupling resonances in the system [1–8]. Investigation of this instability in nonlinear conditions shows that, close to the upper limit and at the center of the instability region, stabilization occurs at amplitudes no larger than the cross-sectional radius r_o of the beam. This offers the possibility of eliminating particle loss due to instability. However, final elucidation of the problem of losses requires the investigation of the transverse oscillations of individual particles in the ring, which may lead, in conditions of instability development, to additional increase in the transverse dimensions of the beam.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 51–56, Ocotber, 1981.     

Consistency of field equations in “Self-Creation” cosmologies

It is pointed out that the field equations in one of Barber's two self-creation cosmologies are not only in disagreement with experiment, but are actually inconsistent, in general. The construction of consistent general relativistic field equations involving field variables, such as, without invoking Lagrangian techniques, requires careful checking that sufficient functional freedom has been provided so as to produce a consistent set of equations.     

Particles and “bumps” in quantum field configurations

We study an approach to making a precise identification of particles with bumps in quantum field configurations. The problem requires some effort because typical field configurations are distributions and not elements of the classical configuration space at all. We show that the part of a configuration consisting of vacuum fluctuations may be identified and filtered out in a very natural way, leaving a function which is in the classical configuration space. The filtered field configuration depends on the state of the field, and for ann-particle state withn particles well localized and well separated in the Newton-Wigner sense, the filtered field configuration hasn bumps located where the particles are. We close with a discussion of observation in the Schrödinger representation for the free field in terms of our results.This paper is dedicated to the memory of Paola Calderoni.     

Large scale magnetic field influence on trap recharging waves in InP:Fe and GaAs:Cr

An impressive linear influence of a magnetic field on optically generated trap-recharging waves (TRW) has been observed in InP:Fe and GaAs:Cr. The phenomenon appears for the particular orientation of parallel to the samples’ surface and orthogonal to the direction of the electric field and wave vector of the TRW . The results are qualitatively explained taking into account the Lorentz force and a pronounced inhomogeneity of the charge transport and of the TRW parameters.     

The two independent equations of circuits in integral form of field theory:The fundamental law of circuits

1 Introduction Historically, circuit theory was initially considered as a part of the electromagnetic theory. Later on, it branched out to become an independent theory. After several stages of its development, Kirchhoff’s law was commonly regarded as the fundamental law of circuits[1]. Especially after the 1960s, the completely topological formulation of Kirchhoff’s law made even more important contribution to the development of moderncircuit theory. However, it has been also known for a l…