Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].     

Aesthetic fields—Null theory

We have studied aesthetic field theory in the case where all invariants constructed from Γ _jk ⁱ and involving g _ij are zero. We studied such a “null” theory in 1972, but the cases we cited were plagued with singularities. By introducing complex fields the situation with respect to singularities improved. Complex fields are consistent with the basic “aesthetic principles” we outlined earlier. Within our null theory we see in two-dimensional spacetime a scattering of particles that was more involved than what we had seen before (regardless of dimensions). We see creation and annihilation of particles out of the vacuum. We also see a three-particle system within a small region of spacetime. In three spacetime dimensions we see a bound two-particle system. Another solution suggests a bound three-particle system. As well as we can tell the particles stay together (confinement) and do not give problems with attenuation. We observe in three dimensions one of the bound systems moving along a definite path in time. The four-dimensional spacetime results are not clear at this point. Whether “topological” bound systems of three particles exist has yet to be determined. A map in the four-dimensional case indicates a planar three maxminima confluence and the suggestion of a second such confluence.     

Many-body theory of π electron systems

Many-body perturbation theory is developed within the dielectric function method presented in a preceding paper [15]. We have explicitly considered the local field corrections (which are disregarded in the random phase approximation) to the self consistent field. These corrections are of second order in the density-density correlation function x and are evaluated exactly in the framework of the adopted approximation scheme because all the integrals which appear in the expressions can be evaluated analytically. Here the method is applied to π electron systems within the zero differential overlap approximation ; explicit calculations of the excitation energies of the benzene molecule using different parametrizations are presented. Comparison is made with results obtained in the RPA and other schemes.     

Semi-gross theory of nuclear β-decay

The gross theory of β-decay is refined to take into account shell effects of the parent nuclei, and the resulting theory is named semi-gross theory. In this theory, the one-particle energy distribution in the parent nucleus is taken to have structures, and the one-particle strength function is assumed to depend on the quantum numbers of the initial state of the decaying nucleon. β-decay (partial) half-lives are calculated for 1659 nuclides, and the results are compared with experimental data as well as with those calculated by the gross theory. The β-decay strength functions are shown for two selected nuclides, and briefly discussed. These numerical studies confirm that the semi-gross theory includes some part of the shell effects correctly, although there still remain deviations of the theoretical results from experimental data, which should, at least partly, be due to shell effects of the daughter nuclei. Comparison of the present results with microscopic theories shows that the overall accuracy of the semi-gross theory is comparable with those of the microscopic theories.     

Aesthetic fields—Null theory II

We have again studied a null theory within the complex aesthetic field theory. This time we required that the spatially inverted origin point data represent the imaginary part of the complex origin point data. This was not the case in our previous studies of the null aesthetic field theory. However, this procedure did not lead to effects not previously observed as far as we could tell. Adding an additional term to the origin point data that presented the null character of the theory also did not lead to new effects. We also investigated a real null theory that led to constant fields. This theory was then made complex by a procedure discussed in the early part of the paper. We found that the resulting complex theory remained trivial nevertheless. Again, we found that it was not necessary for the theory to be null to find confluence type solutions.     

General theory and design of microperforated-panel absorbers

I.Introductionmicroperforated-panelsoundabsorber("microperforated-panelsoundabsorptionconstruc-tion"inearlierpapers,simplified)wasdevelopedinlaternineteensiXtiestoprovidearobustsoundabsorberforsevereenvironments,andtheorywaspresentedlateron[1].AperforatedpanelAsedbeforeasolidsurfaceconstitutestheabsorber,whoseperforationsbeingmadeinsubmillimeters,sothattheperforationsthemselvesprovideenoughacousticresistanceand,atthesametime,sufficientlylowacousticmassreactance,toformawide-bandresonancesoundab…     

Nonlinear gauge theory of Poincaré gravity

A Poincaré affine frame bundle (M) and its associated bundleÊ are established. Using the connection theory of fiber bundles, nonlinear connections on the bundleÊ are introduced as nonlinear gauge fields. An action and two sets of gauge field equations are presented.     

K → πππγ in chiral perturbation theory

We present a complete analysis K → 3ππγ decays to (p ⁴) in the low-energy expansion of the Standard Model. We employ the notion of “generalized bremsstrahlung” to take full advantage of experimental information on the corresponding non-radiative K → 3π decays     

Gell-Mann-Low function in the ϕ4 theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the ?⁴ theory, the algorithm yields the β(g)∝g ^α behavior with α≈1 at large g for the Gell-Mann-Low function.     

“Phonon” scattering beyond perturbation theory

Searching and designing materials with intrinsically low lattice thermal conductivity(LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical-bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T~(-1) relationship(T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.     

Seiberg–Witten theory and matrix models

We derive a family of matrix models which encode solutions to the Seiberg–Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves are the Seiberg–Witten curves of the corresponding theories. In consequence of the geometric engineering, the 5-dimensional case provides a novel matrix model formulation of the topological string theory on a wide class of non-compact toric Calabi–Yau manifolds. This approach also unifies and generalizes other matrix models, such as the Eguchi–Yang matrix model, matrix models for bundles over P¹${\mathbb{P}}^1$, and Chern–Simons matrix models for lens spaces, which arise as various limits of our general result.     

On Painlevé/gauge theory correspondence

We elucidate the relation between Painlevé equations and four-dimensional rank one \(\mathcal {N} = 2\) theories by identifying the connection associated with Painlevé isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated with gauge theories and by studying the corresponding renormalization group flow. Based on this correspondence, we provide long-distance expansions at various canonical rays for all Painlevé \(\tau \)-functions in terms of magnetic and dyonic Nekrasov partition functions for \(\mathcal {N} = 2\) SQCD and Argyres–Douglas theories at self-dual Omega background \(\epsilon _1 + \epsilon _2 = 0\) or equivalently in terms of \(c=1\) irregular conformal blocks.     

The Ginzburg–Landau theory in application

A numerical approach to Ginzburg–Landau (GL) theory is demonstrated and we review its applications to several examples of current interest in the research on superconductivity. This analysis also shows the applicability of the two-dimensional approach to thin superconductors and the re-defined effective GL parameter κ$\kappa$. For two-gap superconductors, the conveniently written GL equations directly show that the magnetic behavior of the sample depends not just on the GL parameter of two bands, but also on the ratio of respective coherence lengths.     

Krein regularization of λφ~3 theory

In this paper, the one-loop self energy of λφ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λφ3 theory in Hilbert space. The self energy is calculated in the one-loop approximation and the result is automatically regularized as a result of "Krein Regularization".     

Leading RG logs in ϕ4 theory

We find the leading RG logs in ϕ⁴ theory for any Feynman diagram with 4 external edges. We obtain the result in two ways. The first way is to calculate the relevant terms in Feynman integrals. The second way is to use the RG invariance based on the Lie algebra of graphs introduced by Connes and Kreimer.     

Luis Santaló and classical field theory

Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional analysis, and also in theoretical physics. Between the 1950’s and the 1970’s, he wrote a series of papers on general relativity and on the attempts at generalizing Einstein’s theory to formulate a unified field theory. His main contribution in this subject was to provide a classification theorem for the plethora of tensors that were populating Einstein’s generalized theory. This paper revisits his work on theoretical physics.

     

Resonance chiral theory for low-energy ππ scattering

The scattering of a pion on a pion in the energy region $\sqrt s $ ≤1 GeV is successfully described on the basis of pole diagrams featuring spinless, spin-1, and spin-2 intermediate particles, provided that the properties of these particles and of their interactions are deduced from the basic principles of QCD and from the requirements of chiral theory.