Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.     

Remarks on Higgs mechanism for gravitons

We construct two kinds of model exhibiting Higgs mechanism for gravitons in potentials of scalar fields. One class of the model is based on a potential which is a generic function of the induced internal metric HAB$H^{AB}$, and the other involves a potential which is a generic function of the usual metric tensor g_μν$g_{\mu \nu }$ and the induced curved metric Y_μν$Y_{\mu \nu }$. In the both models, we derive conditions on the scalar potential in such a way that gravitons acquire mass in a flat Minkowski space–time without non-unitary propagating modes in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. We solve the conditions and find a general solution for the potential. As an interesting specific solution, we present a simple potential for which the Higgs mechanism for gravitons holds in any value of cosmological constant.     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Propagation of Gibbsianness for Infinite-dimensional Gradient Brownian Diffusions

We study the (strong-) Gibbsian character on of the law at time t of an infinite- imensional gradient Brownian diffusion, when the initial distribution is Gibbsian     

Search for minimal quantum group SUq(2) gauge field theory

Different possibilities for the introduction of quantum group gauge fields are discussed. The case of the quantum group SU_q(2) is considered in more detail. We seek for a construction of the quantum group gauge fields which possesses a minimal set of usual c-number fields. It turns out that in this construction the components of the quantum group gauge field take values in the quantum Euclidean space.     

Generalized lattice gauge theory, spin foams and state sum invariants

We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the underlying manifold (≤3, ≤4, any). Ordinary LGT is recovered if the category is the (symmetric) category of representations of a compact Lie group. In the weak coupling limit we recover discretized BF-theory in terms of a coordinate-free version of the spin foam formulation. We work on general cellular decompositions of the underlying manifold.

In particular, we are able to formulate LGT as well as spin foam models of BF-type with quantum gauge group (in dimension ≤4) and with supersymmetric gauge group (in any dimension).

Technically, we express the partition function as a sum over diagrams denoting morphisms in the underlying category. On the LGT side this enables us to introduce a generalized notion of gauge fixing corresponding to a topological move between cellular decompositions of the underlying manifold. On the BF-theory side this allows a rather geometric understanding of the state sum invariants of Turaev/Viro, Barrett/Westbury and Crane/Yetter which we recover.

The construction is extended to include Wilson loop and spin network type observables as well as manifolds with boundaries. In the topological (weak coupling) case this leads to topological quantum field theories with or without embedded spin networks.     

Hamiltonian structure and gauge symmetries of Poincaré gauge theory

This is a review of the constrained dynamical structure of Poincaré gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation laws. As an interesting example of the general approach, we discuss the teleparallel formulation of general relativity.     

Gravitational Waves and the Conformal Transformation

We study the problem of the behaviour of cosmological gravitational waves under conformal transformations. In spite of the apparent triviality of this question, the informations we can obtain from gravitational waves in the so-called Einstein's and Jordan's frame are not the same, mainly with respect to the choice of the initial conditions and of graviton production. The only exception seems to occur in string cosmology due to the duality properties.     

Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ–Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ–Lee term. We find that they cannot.     

Deformation of modulated wave groups in third-order nonlinear media

We present a numerical and analytical investigation of the deformation of a modulated wave group in third-order nonlinear media. Numerical results show that an optical pulse that is initially bichromatic can deform substantially with large variations in amplitude and phase. For specific cases, the bi-chromatic pulse deforms into a train of temporal solitons. Based on the coupled phase-amplitude equation of Nonlinear Schrödinger (NLS), the initial deformation of the modulated wave-packet will be explained and an instability condition can be derived. Energy arguments are given that provide an alternative derivation of the instability condition.     

Expansion of EYM amplitudes in gauge invariant vector space

Motivated by the problem of expanding the single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as a gauge invariant vector space by imposing constraints on the gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in this gauge invariant basis with expansion coefficients being linear combinations of the Yang-Mills amplitude, manifesting the gauge invariance of both the expansion basis and coefficients. With the help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm using several examples.     

BRST invariance in Coulomb gauge QCD

In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ?²${?}^2$, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g⁴)$O\left(g^4\right)$, example.     

光纤多轴应变计

本文介绍了一种用于应变测量的新型元件——光纤多轴应变计。这种元件的测量原理与以往的金属敏感栅测量原理截然不同，测量部分为光信号调制，具有灵敏度高、不受电磁干扰、耐高温、传输距离远等特点。本文对这种应变测量元件做了理论上的分析及实验研究，确定了光纤多轴应变计的测量方案，从而得到点的应力状态。文中还介绍了应变计的测量电路和温度补偿方法。对于这种新型光学应变计来说，作者对其性能与电阻应变片做了初步比较与探讨，这项工作还将继续下去。     

Two dimensional gauge theories revisited

Two dimensional quantum Yang-Mills theory is reexamined using a non-abelian version of the Duistermaat-Heckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressions for intersection pairings on moduli spaces of flat connections on a two dimensional surface. The latter expressions agree, for gauge group SU (2), with formulas obtained recently by several methods.     

On nonlinear gauge theories

In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk–Mr?un and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories.     

Flavor non-universal gauge interactions and anomalies in B-meson decays

Motivated by flavor non-universaity and anomalies in semi-leptonic B-meson decays, we present a general and systematic discussion about how to construct anomaly-free U(1)' gauge theories based on an extended standard model with only three right-handed neutrinos. If all standard model fermions are vector-like under this new gauge symmetry, the most general family non-universal charge assignments,(a,b,c) for three-generation quarks and(d,e,f)for leptons, need satisfy just one condition to be anomaly-free, 3(a+b+c) =-(d+e+f). Any assignment can be linear combinations of five independent anomaly-free solutions. We also illustrate how such models can generally lead to flavor-changing interactions and easily resolve the anomalies in B-meson decays. Probes with B_s-B_s mixing, decay into τ~±, dilepton and dijet searches at colliders are also discussed.     

Analogue of Aharonov-Bohm effect in spin gauge theory

We predict the possibility of observing analogue of the Aharonov-Bohm effect due to long range interaction between spins originating in the framework of spin gauge theory developed earlier. The effect is predicted for both electrons (fermions) and photons. Appropriate experimental set-ups are suggested.     

Opto-electronic displacement gauge based on speckle interferometer

Modern technology demands precise distance measurements. People have used many phenomena for this purpose but there is always a need for less expensive and more reliable devices. In this paper we present a simple opto-electronic distance measurement gauge based on the phenomenon of speckling phenomenon. In the proposed setup we substitute diffraction gratings, which are commonly used in displacement gauges, with a rough surface. When illuminated by a coherent and monochromatic beam the surface scatters light to form a speckle field, whose intensity variations are read by one or more detectors. These changes are related to displacement of the rough surface and, therefore, can be utilized for displacement measurements. The presented setup has some important advantages over the grating approach: lower mechanical tolerances on parts and being based directly on the wavelength of light instead of the period of a grating. Also, it is less expensive, so can offer a viable solution for medium accuracy distance measurements.     

New gauge forces beyond the standard model

In this work we investigate the minimal and next to minimal new gauge forces beyond standard model by constructing the corresponding electroweak chiral Lagrangians. Some phenomenological constraints from the mass differences in the K~0-K~0,B_d~0-B_d~0,B_s~0-B_s~0 systems and the corresponding CP violation parameter are discussed.