317 research outputs found
Canonical form of Euler-Lagrange equations and gauge symmetries
The structure of the Euler-Lagrange equations for a general Lagrangian theory
is studied. For these equations we present a reduction procedure to the
so-called canonical form. In the canonical form the equations are solved with
respect to highest-order derivatives of nongauge coordinates, whereas gauge
coordinates and their derivatives enter in the right hand sides of the
equations as arbitrary functions of time. The reduction procedure reveals
constraints in the Lagrangian formulation of singular systems and, in that
respect, is similar to the Dirac procedure in the Hamiltonian formulation.
Moreover, the reduction procedure allows one to reveal the gauge identities
between the Euler-Lagrange equations. Thus, a constructive way of finding all
the gauge generators within the Lagrangian formulation is presented. At the
same time, it is proven that for local theories all the gauge generators are
local in time operators.Comment: 27 pages, LaTex fil
Canonical and D-transformations in Theories with Constraints
A class class of transformations in a super phase space (we call them
D-transformations) is described, which play in theories with second-class
constraints the role of ordinary canonical transformations in theories without
constraints.Comment: 16 pages, LaTe
Nilpotent noncommutativity and renormalization
We analyze renormalizability properties of noncommutative (NC) theories with
a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model
which is renormalizable at all orders of the loop expansion. We show that this
model has an infrared stable fixed point (at the one-loop level). We check that
the NC QED (which is one-loop renormalizable with usual NC parameter) remains
renormalizable when the NC parameter is bifermionic, at least to the extent of
one-loop diagrams with external photon legs. Our general conclusion is that
bifermionic noncommutativity improves renormalizablility properties of NC
theories.Comment: 5 figures, a reference adde
On Problems of the Lagrangian Quantization of W3-gravity
We consider the two-dimensional model of W3-gravity within Lagrangian
quantization methods for general gauge theories. We use the Batalin-Vilkovisky
formalism to study the arbitrariness in the realization of the gauge algebra.
We obtain a one-parametric non-analytic extension of the gauge algebra, and a
corresponding solution of the classical master equation, related via an
anticanonical transformation to a solution corresponding to an analytic
realization. We investigate the possibility of closed solutions of the
classical master equation in the Sp(2)-covariant formalism and show that such
solutions do not exist in the approximation up to the third order in ghost and
auxiliary fields.Comment: 18 pages, no figure
Superfield extended BRST quantization in general coordinates
We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of
arbitrary gauge theories in general coordinates with the base manifold of
fields and antifields desribed in terms of both bosonic and fermionic
variables.Comment: LaTex, 10 page
Self-adjoint extensions and spectral analysis in the generalized Kratzer problem
We present a mathematically rigorous quantum-mechanical treatment of a
one-dimensional nonrelativistic motion of a particle in the potential field
. For and , the potential is
known as the Kratzer potential and is usually used to describe molecular energy
and structure, interactions between different molecules, and interactions
between non-bonded atoms. We construct all self-adjoint Schrodinger operators
with the potential and represent rigorous solutions of the corresponding
spectral problems. Solving the first part of the problem, we use a method of
specifying s.a. extensions by (asymptotic) s.a. boundary conditions. Solving
spectral problems, we follow the Krein's method of guiding functionals. This
work is a continuation of our previous works devoted to Coulomb, Calogero, and
Aharonov-Bohm potentials.Comment: 31 pages, 1 figur
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