3,739 research outputs found
Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case
This is the first in a series of papers in which we study vertex-algebraic
structure of Feigin-Stoyanovsky's principal subspaces associated to standard
modules for both untwisted and twisted affine Lie algebras. A key idea is to
prove suitable presentations of principal subspaces, without using bases or
even ``small'' spanning sets of these spaces. In this paper we prove
presentations of the principal subspaces of the basic A_1^(1)-modules. These
convenient presentations were previously used in work of
Capparelli-Lepowsky-Milas for the purpose of obtaining the classical
Rogers-Ramanujan recursion for the graded dimensions of the principal
subspaces.Comment: 20 pages. To appear in International J. of Mat
The 3-graviton vertex function in thermal quantum gravity
The high temperature limit of the 3-graviton vertex function is studied in
thermal quantum gravity, to one loop order. The leading () contributions
arising from internal gravitons are calculated and shown to be twice the ones
associated with internal scalar particles, in correspondence with the two
helicity states of the graviton. The gauge invariance of this result follows in
consequence of the Ward and Weyl identities obeyed by the thermal loops, which
are verified explicitly.Comment: 19 pages, plain TeX, IFUSP/P-100
Non-linear electromagnetic interactions in thermal QED
We examine the behavior of the non-linear interactions between
electromagnetic fields at high temperature. It is shown that, in general, the
log(T) dependence on the temperature of the Green functions is simply related
to their UV behavior at zero-temperature. We argue that the effective action
describing the nonlinear thermal electromagnetic interactions has a finite
limit as T tends to infinity. This thermal action approaches, in the long
wavelength limit, the negative of the corresponding zero-temperature action.Comment: 7 pages, IFUSP/P-111
Constructing quantum vertex algebras
This is a sequel to \cite{li-qva}. In this paper, we focus on the
construction of quantum vertex algebras over \C, whose notion was formulated
in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator
algebra (over \C[[h]]) as one of the main motivations. As one of the main
steps in constructing quantum vertex algebras, we prove that every
countable-dimensional nonlocal (namely noncommutative) vertex algebra over
\C, which either is irreducible or has a basis of PBW type, is nondegenerate
in the sense of Etingof and Kazhdan. Using this result, we establish the
nondegeneracy of better known vertex operator algebras and some nonlocal vertex
algebras. We then construct a family of quantum vertex algebras closely related
to Zamolodchikov-Faddeev algebras.Comment: 37 page
Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra
The construction of a q-deformed N=2 superconformal algebra is proposed in
terms of level 1 currents of quantum affine
Lie algebra and a single real Fermi field. In particular, it suggests the
expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its
constituents generate two isomorphic quadratic algebraic structures. The
generalization to is also proposed.Comment: AMSLATEX, 21page
Hard thermal effective action in QCD through the thermal operator
Through the application of the thermal operator to the zero temperature
retarded Green's functions, we derive in a simple way the well known hard
thermal effective action in QCD. By relating these functions to forward
scattering amplitudes for on-shell particles, this derivation also clarifies
the origin of important properties of the hard thermal effective action, such
as the manifest Lorentz and gauge invariance of its integrand.Comment: 6 pages, contribution of the quarks to the effective action included
and one reference added, version to be published in Phys. Rev.
Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures
Results of numerical simulations of a recently derived most general
dissipative-dispersive PDE describing evolution of a film flowing down an
inclined plane are presented. They indicate that a novel complex type of
spatiotemporal patterns can exist for strange attractors of nonequilibrium
systems. It is suggested that real-life experiments satisfying the validity
conditions of the theory are possible: the required sufficiently viscous
liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations
available upon or reques
The Dirac Sea
We give an alternate definition of the free Dirac field featuring an explicit
construction of the Dirac sea. The treatment employs a semi-infinite wedge
product of Hilbert spaces. We also show that the construction is equivalent to
the standard Fock space construction.Comment: 7 page
Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis
We analyse the efficiency of several simulation methods which we have
recently proposed for calculating rate constants for rare events in stochastic
dynamical systems, in or out of equilibrium. We derive analytical expressions
for the computational cost of using these methods, and for the statistical
error in the final estimate of the rate constant, for a given computational
cost. These expressions can be used to determine which method to use for a
given problem, to optimize the choice of parameters, and to evaluate the
significance of the results obtained. We apply the expressions to the
two-dimensional non-equilibrium rare event problem proposed by Maier and Stein.
For this problem, our analysis gives accurate quantitative predictions for the
computational efficiency of the three methods.Comment: 19 pages, 13 figure
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