Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition

The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the flow of the marginal couplings is studied. Our results indicate that higher-derivative terms of the color-unit-vector $\mathbf{n}$ field are necessary for the description of topologically stable knotlike solitons which have been conjectured to be the large-distance degrees of freedom.Comment: 15 pages, no figures, v2: minor improvements, one reference added, version to appear in PR

Linearized Quantum Gravity Using the Projection Operator Formalism

The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a flat background. As a result of the coordinate independence and linear truncation of the perturbation series, the constraint algebra surprisingly becomes partially second-class in both the classical and quantum pictures after all secondary constraints are considered. While new features emerge in the constraint structure, the end result is the same as previously reported: the (separable) physical Hilbert space still only depends on the transverse-traceless degrees of freedom.Comment: 30 pages, no figures, enlarged and corrected versio

Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory

Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon condensate is postulated. The minima are connected to each other by the parity transformations and Weyl group transformations associated with the color su(3) algebra. The presence of degenerated discrete minima in the effective potential leads to the solutions of the effective Euclidean equations of motion in the form of the kink-like gauge field configurations interpolating between different minima. Spectrum of charged scalar field in the kink background is discussed.Comment: 10 pages, 1 figure, added references for sections 1 and

Physical interpretation of the correlation between multi-angle spectral data and canopy height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally

Yang-Mills Fields Quantization in the Factor Space

The perturbation theory over inverse interaction constant $1/g$ is constructed for Yang-Mills theory. It is shown that the new perturbation theory is free from the gauge ghosts and Gribov's ambiguities, each order over $1/g$ presents the gauge-invariant quantity. It is remarkable that offered perturbation theory did not contain divergences, at least in the vector fields sector, and no renormalization procedure is necessary for it.Comment: 27 pages, Latex, no figure

Gribov Problem for Gauge Theories: a Pedagogical Introduction

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear differential equation, and the various solutions of such a non-linear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.Comment: 24 pages, Revtex 4. In the revised version, a statement has been amended on page 11, and References 14, 16 and 27 have been improve

Оценка уникальности популяций Bufo Viridis (Amphibia: Anura) с точки зрения рациональной экологической этики

Substantive provisions of rational environmental ethics are stated. This concept presumes to compare a level of uniqueness of different objects, which forms the establishment for giving the ethical value. The developed approach is used for comparison of 26 populations of Bufo viridis Laurenti, 1768 from Left-bank forest-steppe of Ukraine. Узагальнено основні положення раціональної екологічної етики. Ця концепція може дозволити порівнювати рівень унікальності різних об’єктів, стати основою для визнання їх етичної цінності. Даний підхід застосований для порівняння 26 популяцій зеленої ропухи (Bufo viridis Laurenti, 1768) з Лівобережного Лісостепу України. Узагальнено основні положення раціональної екологічної етики. Ця концепція може дозволити порівнювати рівень унікальності різних об’єктів, стати основою для визнання їх етичної цінності. Даний підхід застосований для порівняння 26 популяцій зеленої ропухи (Bufo viridis Laurenti, 1768) з Лівобережного Лісостепу України.

Monopoles and Knots in Skyrme Theory

We show that the Skyrme theory actually is a theory of monopoles which allows a new type of solitons, the topological knots made of monopole-anti-monopole pair,which is different from the well-known skyrmions. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infra-red limit. We discuss the physical implications of our results.Comment: 4 pages. Phys. Rev. Lett. in pres

Lagrangian and Hamiltonian Formalism on a Quantum Plane

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on $TQ_{q,p}$. These two differential calculi can in principle give rise to two different particle dynamics, starting from a single Lagrangian. For Hamiltonian mechanics, we define a phase space $T^*Q_{q,p}$ spanned by noncommuting particle coordinates and momenta. The commutation relations for the momenta can be determined only after knowing their functional dependence on coordinates and velocities. Thus these commutation relations, as well as the differential calculus on $T^*Q_{q,p}$, depend on the initial choice of Lagrangian. We obtain the deformed Hamilton's equations of motion and the deformed Poisson brackets, and their definitions also depend on our initial choice of Lagrangian. We illustrate these ideas for two sample Lagrangians. The first system we examine corresponds to that of a nonrelativistic particle in a scalar potential. The other Lagrangian we consider is first order in time derivative

Dynamics in a noncommutative phase space

Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using this, both the Hamiltonian and Lagrangian forms of dynamics have been constructed. In contrast to earlier forms of $q$-dynamics, our formalism has the advantage of preserving the conventional symmetries such as rotational or Lorentz invariance.Comment: LaTeX-twice, 16 page