1,616 research outputs found
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
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
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
Yang-Mills Fields Quantization in the Factor Space
The perturbation theory over inverse interaction constant 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
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
Impact of Heat Resources on Rice Productivity in the Sarpinsky Lowland
The possibility of rice cultivation in the northern areas of rice sowing is determined by the sum of effective air temperatures (Σt ≥ 15 ∘C) over the growing season and its distribution over the vegetation phases of the plants. A long-term statistical and correlation analysis of rice productivity depending on the thermal resources of the Sarpinsky lowland at the Maliye Derbeta meteorological station for the period from 1964 to 2018 (correlation coefficient r = 0.68) is given. It is established that the sum of effective air temperatures varies from 3140.2 to 3999.7 ∘C, while the average annual value is 2820 ∘C. The highest yield (more than 5 t/ha) of rice grains is formed in years with the sum of effective temperatures over 3000 ∘C. The fluctuations of air temperature and their influence on the production process, and the yield of rice grains are analyzed, the results of which can be used as source data in modeling climate change scenarios and predicting rice grain production. The optimal amounts of effective air temperatures for the period April-September, ensuring the realization of the potential productivity of rice in the Sarpinsky lowland conditions, are determined
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 . For Lagrangian mechanics, we
first define a tangent quantum plane spanned by noncommuting
particle coordinates and velocities. Using techniques similar to those of Wess
and Zumino, we construct two different differential calculi on .
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 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
, 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
. The -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 -dynamics,
our formalism has the advantage of preserving the conventional symmetries such
as rotational or Lorentz invariance.Comment: LaTeX-twice, 16 page
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
The Inverse Variational Problem for Autoparallels
We study the problem of the existence of a local quantum scalar field theory
in a general affine metric space that in the semiclassical approximation would
lead to the autoparallel motion of wave packets, thus providing a deviation of
the spinless particle trajectory from the geodesics in the presence of torsion.
The problem is shown to be equivalent to the inverse problem of the calculus of
variations for the autoparallel motion with additional conditions that the
action (if it exists) has to be invariant under time reparametrizations and
general coordinate transformations, while depending analytically on the torsion
tensor. The problem is proved to have no solution for a generic torsion in
four-dimensional spacetime. A solution exists only if the contracted torsion
tensor is a gradient of a scalar field. The corresponding field theory
describes coupling of matter to the dilaton field.Comment: 13 pages, plain Latex, no figure
Phase spaces related to standard classical -matrices
Fundamental representations of real simple Poisson Lie groups are Poisson
actions with a suitable choice of the Poisson structure on the underlying
(real) vector space. We study these (mostly quadratic) Poisson structures and
corresponding phase spaces (symplectic groupoids).Comment: 20 pages, LaTeX, no figure
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