104 research outputs found
Supersymmetric Gauge Theories in Twistor Space
We construct a twistor space action for N=4 super Yang-Mills theory and show
that it is equivalent to its four dimensional spacetime counterpart at the
level of perturbation theory. We compare our partition function to the original
twistor-string proposal, showing that although our theory is closely related to
string theory, it is free from conformal supergravity. We also provide twistor
actions for gauge theories with N<4 supersymmetry, and show how matter
multiplets may be coupled to the gauge sector.Comment: 23 pages, no figure
Long Cycles in a Perturbed Mean Field Model of a Boson Gas
In this paper we give a precise mathematical formulation of the relation
between Bose condensation and long cycles and prove its validity for the
perturbed mean field model of a Bose gas. We decompose the total density
into the number density of
particles belonging to cycles of finite length () and to
infinitely long cycles () in the thermodynamic limit. For
this model we prove that when there is Bose condensation,
is different from zero and identical to the condensate density. This is
achieved through an application of the theory of large deviations. We discuss
the possible equivalence of with off-diagonal long
range order and winding paths that occur in the path integral representation of
the Bose gas.Comment: 10 page
Introduction to Loop Quantum Gravity
This article is based on the opening lecture at the third quantum geometry
and quantum gravity school sponsored by the European Science Foundation and
held at Zakopane, Poland in March 2011. The goal of the lecture was to present
a broad perspective on loop quantum gravity for young researchers. The first
part is addressed to beginning students and the second to young researchers who
are already working in quantum gravity.Comment: 30 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:gr-qc/041005
Large deviations for many Brownian bridges with symmetrised initial-terminal condition
Consider a large system of Brownian motions in with some
non-degenerate initial measure on some fixed time interval with
symmetrised initial-terminal condition. That is, for any , the terminal
location of the -th motion is affixed to the initial point of the
-th motion, where is a uniformly distributed random
permutation of . Such systems play an important role in quantum
physics in the description of Boson systems at positive temperature .
In this paper, we describe the large-N behaviour of the empirical path
measure (the mean of the Dirac measures in the paths) and of the mean of
the normalised occupation measures of the motions in terms of large
deviations principles. The rate functions are given as variational formulas
involving certain entropies and Fenchel-Legendre transforms. Consequences are
drawn for asymptotic independence statements and laws of large numbers.
In the special case related to quantum physics, our rate function for the
occupation measures turns out to be equal to the well-known Donsker-Varadhan
rate function for the occupation measures of one motion in the limit of
diverging time. This enables us to prove a simple formula for the large-N
asymptotic of the symmetrised trace of , where
is an -particle Hamilton operator in a trap
Complex Kerr Geometry and Nonstationary Kerr Solutions
In the frame of the Kerr-Schild approach, we consider the complex structure
of Kerr geometry which is determined by a complex world line of a complex
source. The real Kerr geometry is represented as a real slice of this complex
structure. The Kerr geometry is generalized to the nonstationary case when the
current geometry is determined by a retarded time and is defined by a
retarded-time construction via a given complex world line of source. A general
exact solution corresponding to arbitrary motion of a spinning source is
obtained. The acceleration of the source is accompanied by a lightlike
radiation along the principal null congruence. It generalizes to the rotating
case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in
PRD), added the relation to twistors and algorithm of numerical computations,
English is correcte
Looking back at superfluid helium
A few years after the discovery of Bose Einstein condensation in several
gases, it is interesting to look back at some properties of superfluid helium.
After a short historical review, I comment shortly on boiling and evaporation,
then on the role of rotons and vortices in the existence of a critical velocity
in superfluid helium. I finally discuss the existence of a condensate in a
liquid with strong interactions, and the pressure variation of its superfluid
transition temperature.Comment: Conference "Bose Einstein Condensation", Institut henri Poincare,
Paris, 29 march 200
Einstein energy associated with the Friedmann -Robertson -Walker metric
Following Einstein's definition of Lagrangian density and gravitational field
energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A.,
Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I.
Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general
formula for the total matter plus gravitational field energy () of an
arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C.,
{\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962));
Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in
quasi-Cartesian coordinates, this formula leads to the well known result , where is the
determinant of the metric tensor and is the energy momentum tensor of
the {\em matter}. Though in the literature, this is known as "Tolman Mass", it
must be realized that this is essentially "Einstein Mass" because the
underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz
obtained the same expression for the "inertial mass" of a static isolated
system without using any pseudo-tensor at all and which points to physical
significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz,
E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed.,
1962)! For the first time we apply this general formula to find an expression
for for the Friedmann- Robertson -Walker (FRW) metric by using the same
quasi-Cartesian basis. As we analyze this new result, physically, a spatially
flat model having no cosmological constant is suggested. Eventually, it is seen
that conservation of is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the
journal version is uploade
Unwrapping Closed Timelike Curves
Closed timelike curves (CTCs) appear in many solutions of the Einstein
equation, even with reasonable matter sources. These solutions appear to
violate causality and so are considered problematic. Since CTCs reflect the
global properties of a spacetime, one can attempt to change its topology,
without changing its geometry, in such a way that the former CTCs are no longer
closed in the new spacetime. This procedure is informally known as unwrapping.
However, changes in global identifications tend to lead to local effects, and
unwrapping is no exception, as it introduces a special kind of singularity,
called quasi-regular. This "unwrapping" singularity is similar to the string
singularities. We give two examples of unwrapping of essentially 2+1
dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. We
show that the unwrapped Gott spacetime, while singular, is at least devoid of
CTCs. In contrast, the unwrapped Godel spacetime still contains CTCs through
every point. A "multiple unwrapping" procedure is devised to remove the
remaining circular CTCs. We conclude that, based on the two spacetimes we
investigated, CTCs appearing in the solutions of the Einstein equation are not
simply a mathematical artifact of coordinate identifications, but are indeed a
necessary consequence of General Relativity, provided only that we demand these
solutions do not possess naked quasi-regular singularities.Comment: 29 pages, 9 figure
Anisotropic Conformal Infinity
We generalize Penrose's notion of conformal infinity of spacetime, to
situations with anisotropic scaling. This is relevant not only for
Lifshitz-type anisotropic gravity models, but also in standard general
relativity and string theory, for spacetimes exhibiting a natural asymptotic
anisotropy. Examples include the Lifshitz and Schrodinger spaces (proposed as
AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the
near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears
crucial for resolving puzzles of holographic renormalization in such
spacetimes.Comment: 11 page
The arrow of time: from universe time-asymmetry to local irreversible processes
In several previous papers we have argued for a global and non-entropic
approach to the problem of the arrow of time, according to which the ''arrow''
is only a metaphorical way of expressing the geometrical time-asymmetry of the
universe. We have also shown that, under definite conditions, this global
time-asymmetry can be transferred to local contexts as an energy flow that
points to the same temporal direction all over the spacetime. The aim of this
paper is to complete the global and non-entropic program by showing that our
approach is able to account for irreversible local phenomena, which have been
traditionally considered as the physical origin of the arrow of time.Comment: 48 pages, 8 figures, revtex4. Accepted for publication in Foundations
of Physic
- …