Optimizedδ — expansion and triviality or non-triviality of field theories

We use a very simple version of the optimized (linear)δ-expansion by scaling the free part of the Lagrangian with a variational parameter. This method is well suited to calculate the renormalized coupling constant in terms of the free one and the cutoff. One never has to calculate any new Feynman graphs but simply can modify existing results from the literature. We find that Φ ₄ ⁴ -theory as well as QED are free in the limit where the cutoff goes to infinity. In contrast to this, the structure of Yang-Mills theories enforces a special choice of the Lagrangian of theδ-expansion. Together with the change in the sign of theβ-function, this leads to a different behavior and allows Yang-Mills theory to become non trivial.     

On Batalin–Vilkovisky formalism of non-commutative field theories

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes–Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra–Itzykson–Zuber integral.     

A class of 6D conformal field theories: relation to 4D superconformal Yang-Mills theories?

We describe a class of six-dimensional conformal field theories that possibly are related to the tensionless string theories. They have an ADE classification, but no other discrete or continuous parameters, with the A(N-1) theory arising by factoring out the collective "center of mass" degrees of freedom from N noninteracting chiral two-forms. The Hilbert space carries an irreducible representation of the same Heisenberg group that appears in the tensionless string theories, and the "Wilson surface" observables obey the same superselection rules. When compactified on a two-torus, our theories have the same behavior under S duality as N = 4 super Yang-Mills theories.     

A new proof of the existence and nontriviality of the continuum ϕ 2 4 and ϕ 3 4 quantum field theories

We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum ? ₂ ⁴ and ? ₃ ⁴ quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ² for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.     

Replica field theories,painlevé transcendents,and exact correlation functions

Exact solvability is claimed for nonlinear replica sigma models derived in the context of random matrix theories. Contrary to other approaches reported in the literature, the framework outlined does not rely on traditional "replica symmetry breaking" but rests on a previously unnoticed exact relation between replica partition functions and Painlevé transcendents. While expected to be applicable to matrix models of arbitrary symmetries, the method is used to treat fermionic replicas for the Gaussian unitary ensemble (GUE), chiral GUE (symmetry classes A and AIII in Cartan classification) and Ginibre's ensemble of complex non-Hermitian random matrices. Further applications are briefly discussed.     

Inverse scattering and solitons in An − 1 affine Toda field theories II

New single soliton solutions to the affine Toda field theories are constructed, exhibiting previously unobserved topological charges. This goes some of the way in filling the weights of the fundamental representations, but nevertheless holes in the representations remain. We use the group double-cross product form of the inverse scattering method, and restrict ourselves to the rank-one solutions.     

Phantom expansion with non-linear Schrödinger-type formulation of scalar field cosmology

We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schrödinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of Schrödinger quantities as similar to those in time-independent quantum mechanics. We assume the expansion to be superfast, i.e. phantom expansion. We report all Schrödinger-analogous quantities to scalar field cosmology. Effective equation of state coefficient is analyzed and illustrated. We show that in a non-flat universe, there is no fixed w _eff value for the phantom divide. In a non-flat universe, even w _eff > ?1, the expansion can be phantom. Moreover, in open universe, phantom expansion can happen even with w _eff > 0. We also report scalar field exact solutions within frameworks of the Friedmann formulation and the NLS formulation in non-flat universe cases.     

Lax connections in T■-deformed integrable field theories

In this work,we attempt to construct the Lax connections of TT-deformed integrable field theories in two different ways.With reasonable assumptions,we make an ansatz and find the Lax pairs in the TT-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly.This method is straightforward,but it may be difficult to apply for general models.We then make use of a dynamic coordinate transformation to read the Lax connection in the deformed theory from the undeformed one.We find that once the inverse of the transformation is available,the Lax connection can be read easily.We show the construction explicitly for a few classes of scalar models and find consistency with those determined using the first method.     

Point to string transformation,or framedependent notion of “locality”: An attempt to finitize field theories including gravitation

A novel approach has been made to the divergence problem in local field theories, in which the notion of locality is still retained but loses its absolute meaning, just like simultaneity. The basic idea is to introduce a pure-imaginary elementary length into 3-dimensional space, while keeping time structureless so as to retain the unitarity of theS-matrix. Consequently, light becomes dispersive at sufficiently short wavelengths, and Lorentz transformation becomes a point-to-string transformation. When reformulated to meet the new Lorentz invariance, all the localfield (in the above sense) theories in a flat space become finite,while retaining their conventional form. This has been demonstrated by the derivation of finitized Coulomb potential and correct high-momentum behavior of quantum-electrodynamic coupling constant. For diagrams including gravitons, evaluation of the superficial degrees of divergence shows that only a restricted number of 1-(and 2-) loop diagrams might be divergent, while those of more than 3 loops are definitely convergent, thus indicating possible renormalizability (or something better) of quantum gravity in Einstein's formalism of general relativity. Since 4-dimensional simple supergravity removes 1-and 2-loop divergence, a combination of the theory and the present one might lead to a more interesting result.     

Periodic solutions of massive φ 4 and Yang-Mills theories

The well-known connection between the SU(2) gauge theory and the massless ⁴ theory is extended to theories with nonzero mass. Elliptic solutions of these massive theories are given. These are of the plane-wave variety, with independent variable u=p·x where p is a constant four-vector. They depend on a free parameter k. Two of the solutions are generalized plane-waves while the third describes fluctuations about the vacuum solution.     

C-disorder fields and Γ(2)-invariant partition functions in parafermionic conformal field theories

The character formulae for the C-disorder fields corresponding to the charge conjugation symmetry in the parafermionic conformal field theories of Zamolodchikov and Fateev are obtained. These characters span a unitary representation of the level 2 subgroup Γ(2) of the full modular group. The corresponding Γ(2)-invariant partition functions are calculated. Derivation of the character formula is based on the relation between the parafermionic theories and the twisted N = 2 superconformal algebra. A similar idea is applied to explicitly construct the highest weight modules of the twisted SU(2) Kac-Moody algebra.     

Off-shell d=10, N=1 Poincaré supergravity and the embeddibility of higher-derivative field theories in superspace

The constraints on the supertorsion are presented which lead to off-shell d=10, N=2 Poincaré supergravity and the superfluids which are known to enter the superspace action are identified. It is pointed out that Poincaré off-shell constraints have to be used in a superspace formulation of the low-energy effective actions of N=1 superstrings. However, current formulations of N=1 superstrings propagating in arbitrary supergravity backgrounds are incompatible with these off-shell constraints.     

Influence of ambient pressure on properties and expansion of laser-induced plasma

A Nd:YAG pulsed laser is used to ablate HgCdTe target at different ambient pressures, the emission spectrum is detected by a time- and space-resolved diagnostic technique. It is found that the characteristics of time-resolved emission spectra are influenced by the pressure of background gas. A theoretical model is developed to investigate expansion mechanism of plasma, the time evolution of the propagation distances and the velocities of plasma plume are calculated by the model at pressures of 1.01×105, 1000, and 5 Pa, respectively. The calculated results are well consistent with the experimental data.     

Optimized design of parallel beam-splitting prism

A large lateral shearing distance of parallel beam-splitting prism is often needed in laser modulation and polarization interference. In this letter, we present an optimized design of parallel beam-splitting prism and list some different cases in detail. The optimized design widens the use range of parallel beam-splitting prism. At the wavelength of 632.8 nm, the law that the enlargement ratio changes with the refractive index and the apex angle is verified.     

Optimized Design and Fabrication of Mach–Zehnder Interferometer Sensor in Polymer Technology

Abstract

Without any external modulating facilities, through a precisely controlled sensing length of 11,515 μm, the integrated Mach–Zehnder interferometer sensor obtains a quadrature point and linear response in refractive index measuring range of 1.31–1.42 at the wavelength of 1,550 nm. Combined with structure optimization and surface treatment of sensing arm, the sensitivity is measured as 225.4 dB/RIU, and the sensing response time is less than 20 s to analyte solutions. Cost-efficient polymers are used as waveguide materials, and a microfluidic system is achieved.