3,722 research outputs found
Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity
This review contains a summary of work by J.-L. Gervais and the author on the
operator approach to 2d gravity. Special emphasis is placed on the construction
of local observables -the Liouville exponentials and the Liouville field itself
- and the underlying algebra of chiral vertex operators. The double quantum
group structure arising from the presence of two screening charges is discussed
and the generalized algebra and field operators are derived. In the last part,
we show that our construction gives rise to a natural definition of a quantum
tau function, which is a noncommutative version of the classical
group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference
on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199
Operator Coproduct-Realization of Quantum Group Transformations in Two Dimensional Gravity, I.
A simple connection between the universal matrix of (for
spins \demi and ) and the required form of the co-product action of the
Hilbert space generators of the quantum group symmetry is put forward. This
gives an explicit operator realization of the co-product action on the
covariant operators. It allows us to derive the quantum group covariance of the
fusion and braiding matrices, although it is of a new type: the generators
depend upon worldsheet variables, and obey a new central extension of
realized by (what we call) fixed point commutation relations. This
is explained by showing that the link between the algebra of field
transformations and that of the co-product generators is much weaker than
previously thought. The central charges of our extended algebra,
which includes the Liouville zero-mode momentum in a nontrivial way are related
to Virasoro-descendants of unity. We also show how our approach can be used to
derive the Hopf algebra structure of the extended quantum-group symmetry
U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the
screening charges of 2D gravity.Comment: 33 pages, latex, no figure
The Multivalued Free-Field Maps of Liouville and Toda Gravities
Liouville and Toda gravity theories with non-vanishing interaction potentials
have spectra obtained by dividing the free-field spectra for these cases by the
Weyl group of the corresponding or Lie algebra. We study the
canonical transformations between interacting and free fields using the
technique of intertwining operators, giving explicit constructions for the
wavefunctions and showing that they are invariant under the corresponding Weyl
groups. These explicit constructions also permit a detailed analysis of the
operator-state maps and of the nature of the Seiberg bounds.Comment: 47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging
to permit Postscript generation, no changes to pape
Quantum Canonical Transformations revisited
A preferred form for the path integral discretization is suggested that
allows the implementation of canonical transformations in quantum theory.Comment: 8 pages, LaTe
Lotka--Volterra Type Equations and their Explicit Integration
In the present note we give an explicit integration of some
two--dimensionalised Lotka--Volterra type equations associated with simple Lie
algebras, other than the familiar case, possessing a representation
without branching. This allows us, in particular, to treat the first
fundamental representations of , , , and on the same
footing.Comment: 3 pages LATEX fil
Defectors cannot be detected during"small talk" with strangers.
To account for the widespread human tendency to cooperate in one-shot social dilemmas, some theorists have proposed that cooperators can be reliably detected based on ethological displays that are difficult to fake. Experimental findings have supported the view that cooperators can be distinguished from defectors based on "thin slices" of behavior, but the relevant cues have remained elusive, and the role of the judge's perspective remains unclear. In this study, we followed triadic conversations among unacquainted same-sex college students with unannounced dyadic one-shot prisoner's dilemmas, and asked participants to guess the PD decisions made toward them and among the other two participants. Two other sets of participants guessed the PD decisions after viewing videotape of the conversations, either with foreknowledge (informed), or without foreknowledge (naïve), of the post-conversation PD. Only naïve video viewers approached better-than-chance prediction accuracy, and they were significantly accurate at predicting the PD decisions of only opposite-sexed conversation participants. Four ethological displays recently proposed to cue defection in one-shot social dilemmas (arms crossed, lean back, hand touch, and face touch) failed to predict either actual defection or guesses of defection by any category of observer. Our results cast doubt on the role of "greenbeard" signals in the evolution of human prosociality, although they suggest that eavesdropping may be more informative about others' cooperative propensities than direct interaction
Reparametrization Invariance of Path Integrals
We demonstrate the reparametrization invariance of perturbatively defined
one-dimensional functional integrals up to the three-loop level for a path
integral of a quantum-mechanical point particle in a box. We exhibit the origin
of the failure of earlier authors to establish reparametrization invariance
which led them to introduce, superfluously, a compensating potential depending
on the connection of the coordinate system. We show that problems with
invariance are absent by defining path integrals as the epsilon-> 0 -limit of
1+ epsilon -dimensional functional integrals.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re289/preprint.htm
Light-Cone Quantization of the Liouville Model
We present the quantization of the Liouville model defined in light-cone
coordinates in (1,1) signature space. We take advantage of the representation
of the Liouville field by the free field of the Backl\"{u}nd transformation and
adapt the approch by Braaten, Curtright and Thorn.
Quantum operators of the Liouville field ,
, , are constructed consistently in
terms of the free field. The Liouville model field theory space is found to be
restricted to the sector with field momentum , , which
is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6
Domain Walls in a FRW Universe
We solve the equations of motion for a scalar field with domain wall boundary
conditions in a Friedmann-Robertson-Walker (FRW) spacetime. We find (in
agreement with Basu and Vilenkin) that no domain wall solutions exist in de
Sitter spacetime for h = H/m >= 1/2, where H is the Hubble parameter and m is
the scalar mass. In the general FRW case we develop a systematic perturbative
expansion in h to arrive at an approximate solution to the field equations. We
calculate the energy momentum tensor of the domain wall configuration, and show
that the energy density can become negative at the core of the defect for some
values of the non-minimal coupling parameter xi. We develop a translationally
invariant theory for fluctuations of the wall, obtain the effective Lagrangian
for these fluctuations, and quantize them using the Bunch-Davies vacuum in the
de Sitter case. Unlike previous analyses, we find that the fluctuations act as
zero-mass (as opposed to tachyonic) modes. This allows us to calculate the
distortion and the normal-normal correlators for the surface. The normal-normal
correlator decreases logarithmically with the distance between points for large
times and distances, indicating that the interface becomes rougher than in
Minkowski spacetime.Comment: 23 pages, LaTeX, 7 figures using epsf.tex. Now auto-generates P
- …