1,262 research outputs found
Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra
With slight modifications in the zero modes contributions, the positive and
negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can
be put together to form a single algebra which can be regarded as an elliptic
deformation of the universal enveloping algebra of \hat{g}, where g is any
classical simply-laced Lie algebra.Comment: LaTeX file, 9 pages. Errors in Serre relation corrected. Two
references to Awata,H. et al adde
Vertex Operators for Deformed Virasoro Algebra
Vertex operators for the deformed Virasoro algebra are defined, their bosonic
representation is constructed and difference equation for the simplest vertex
operators is described.Comment: stylistic errors correcte
Dynamics of Symmetry Breaking and Tachyonic Preheating
We reconsider the old problem of the dynamics of spontaneous symmetry
breaking using 3d lattice simulations, and develop a theory of tachyonic
preheating, which occurs due to the spinodal instability of the scalar field.
Tachyonic preheating is so efficient that symmetry breaking typically completes
within a single oscillation of the field distribution as it rolls towards the
minimum of its effective potential. As an application of this theory we
consider preheating in the hybrid inflation scenario, including SUSY-motivated
F-term and D-term inflationary models. We show that preheating in hybrid
inflation is typically tachyonic and the stage of oscillations of a homogeneous
component of the scalar fields driving inflation ends after a single
oscillation. Our results may also be relevant for the theory of the formation
of disoriented chiral condensates in heavy ion collisions.Comment: 7 pages, 6 figures. Higher quality figures and computer generated
movies in gif format illustrating our results can be found at
http://physics.stanford.edu/gfelder/hybri
Explicit solution of the (quantum) elliptic Calogero-Sutherland model
We derive explicit formulas for the eigenfunctions and eigenvalues of the
elliptic Calogero-Sutherland model as infinite series, to all orders and for
arbitrary particle numbers and coupling parameters. The eigenfunctions obtained
provide an elliptic deformation of the Jack polynomials. We prove in certain
special cases that these series have a finite radius of convergence in the nome
of the elliptic functions, including the two particle (= Lam\'e) case for
non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low
order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper
completely revised: the results of v1 and v2 are extended to all order
Elliptic Deformed Superalgebra
We introduce the elliptic superalgebra as one
parameter deformation of the quantum superalgebra . For an
arbitrary level we give the bosonization of the elliptic
superalgebra and the screening currents that commute
with modulo total difference.Comment: LaTEX, 25 page
Parametrization of semi-dynamical quantum reflection algebra
We construct sets of structure matrices for the semi-dynamical reflection
algebra, solving the Yang-Baxter type consistency equations extended by the
action of an automorphism of the auxiliary space. These solutions are
parametrized by dynamical conjugation matrices, Drinfel'd twist representations
and quantum non-dynamical -matrices. They yield factorized forms for the
monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on
construction of Hamiltonian
Quantum Group as Semi-infinite Cohomology
We obtain the quantum group as semi-infinite cohomology of the
Virasoro algebra with values in a tensor product of two braided vertex operator
algebras with complementary central charges . Each braided VOA is
constructed from the free Fock space realization of the Virasoro algebra with
an additional q-deformed harmonic oscillator degree of freedom. The braided VOA
structure arises from the theory of local systems over configuration spaces and
it yields an associative algebra structure on the cohomology. We explicitly
provide the four cohomology classes that serve as the generators of
and verify their relations. We also discuss the possible extensions of our
construction and its connection to the Liouville model and minimal string
theory.Comment: 50 pages, 7 figures, minor revisions, typos corrected, Communications
in Mathematical Physics, in pres
On Vertex Operator Construction of Quantum Affine Algebras
We describe the construction of the quantum deformed affine Lie algebras
using the vertex operators in the free field theory. We prove the Serre
relations for the quantum deformed Borel subalgebras of affine algebras, namely
the case of is considered in detail. We provide some
formulas for generators of affine algebra.Comment: LaTeX, 9 pages; typos corrected, references adde
Dynamics of a Dark Matter Field with a Quartic Self-Interaction Potential
It may prove useful in cosmology to understand the behavior of the energy
distribution in a scalar field that interacts only with gravity and with itself
by a pure quartic potential, because if such a field existed it would be
gravitationally produced, as a squeezed state, during inflation. It is known
that the mean energy density in such a field after inflation varies with the
expansion of the universe in the same way as radiation. I show that if the
field initially is close to homogeneous, with small energy density contrast
delta rho /rho and coherence length L, the energy density fluctuations behave
like acoustic oscillations in an ideal relativistic fluid for a time on the
order of L/|delta rho /rho|. This ends with the appearance of features that
resemble shock waves, but interact in a close to elastic way that reversibly
disturbs the energy distribution.Comment: 7 pages, 5 figures, submitted to Phys Rev
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