17 research outputs found
The Ostrogradsky prescription for BFV formalism
Gauge-invariant systems of a general form with higher order derivatives of
gauge parameters are investigated within the framework of the BFV formalism.
Higher order terms of the BRST charge and BRST-invariant Hamiltonian are
obtained. It is shown that the identification rules for Lagrangian and
Hamiltonian ghost variables depend on the choice of the extension of
constraints from the primary constraint surface.Comment: LaTeX, 13 page
BRST formalism for systems with higher order derivatives of gauge parameters
For a wide class of mechanical systems, invariant under gauge transformations
with higher (arbitrary) order time derivatives of gauge parameters, the
equivalence of Lagrangian and Hamiltonian BRST formalisms is proved. It is
shown that the Ostrogradsky formalism establishes the natural rules to relate
the BFV ghost canonical pairs with the ghosts and antighosts introduced by the
Lagrangian approach. Explicit relation between corresponding gauge-fixing terms
is obtained.Comment: 19 pages, LaTeX, no figure
Strings as a Model for Parent and Baby Universes: Total Splitting Rates
Emission of hard microscopic string (graviton) by an excited macroscopic
string may be viewed as a model of branching of a -dimensional baby
universe off large parent one. We show that, apart from a trivial factor, the
total emission rate is not suppressed by the size of the macroscopic string.
This implies unsuppressed loss of quantum coherence in -dimensional
parent universe.Comment: 12 pages, LaTeX, 2 figures (bezier.sty
Highest -Weight Representations and Functional Relations
We discuss highest -weight representations of quantum loop algebras and
the corresponding functional relations between integrability objects. In
particular, we compare the prefundamental and -oscillator representations of
the positive Borel subalgebras of the quantum group for arbitrary values of . Our article has partially
the nature of a short review, but it also contains new results. These are the
expressions for the -operators, and the exact relationship between different
representations, as a byproduct resulting in certain conclusions about
functional relations
Vertex Models and Spin Chains in Formulas and Pictures
We systematise and develop a graphical approach to the investigations of
quantum integrable vertex statistical models and the corresponding quantum spin
chains. The graphical forms of the unitarity and various crossing relations are
introduced. Their explicit analytical forms for the case of integrable systems
associated with the quantum loop algebra are given. The commutativity conditions for the
transfer operators of lattices with a boundary are derived by the graphical
method. Our consideration reveals useful advantages of the graphical approach
for certain problems in the theory of quantum integrable systems
Higher symmetries of Toda equations
The symmetries of the simplest non-abelian Toda equations are discussed. The set of characteristic integrals whose Hamiltonian counterparts form a W -algebra, is presented
Exercises with the universal R-matrix
Using the formula for the universal -matrix proposed by Khoroshkin and
Tolstoy, we give a detailed derivation of -operators for the quantum groups
associated with the generalized Cartan matrices and .Comment: 36 page