215 research outputs found
Covariant Quantum Fields on Noncommutative Spacetimes
A spinless covariant field on Minkowski spacetime \M^{d+1} obeys the
relation where
is an element of the Poincar\'e group \Pg and is its unitary representation on quantum vector states. It
expresses the fact that Poincar\'e transformations are being unitary
implemented. It has a classical analogy where field covariance shows that
Poincar\'e transformations are canonically implemented. Covariance is
self-reproducing: products of covariant fields are covariant. We recall these
properties and use them to formulate the notion of covariant quantum fields on
noncommutative spacetimes. In this way all our earlier results on dressing,
statistics, etc. for Moyal spacetimes are derived transparently. For the Voros
algebra, covariance and the *-operation are in conflict so that there are no
covariant Voros fields compatible with *, a result we found earlier. The notion
of Drinfel'd twist underlying much of the preceding discussion is extended to
discrete abelian and nonabelian groups such as the mapping class groups of
topological geons. For twists involving nonabelian groups the emergent
spacetimes are nonassociative.Comment: 20 page
The Gauss Law: A Tale
The Gauss law plays a basic role in gauge theories, enforcing gauge
invariance and creating edge states and superselection sectors. This article
surveys these aspects of the Gauss law in QED, QCD and nonlinear models.
It is argued that nonabelian superselection rules are spontaneously broken.
That is the case with of colour which is spontaneously broken to
. Nonlinear models are reformulated as gauge theories
and the existence of edge states and superselection sectors in these models is
also established.Comment: Published version. References adde
Non-Pauli Effects from Noncommutative Spacetimes
Noncommutative spacetimes lead to nonlocal quantum field theories (qft's)
where spin-statistics theorems cannot be proved. For this reason, and also
backed by detailed arguments, it has been suggested that they get corrected on
such spacetimes leading to small violations of the Pauli principle. In a recent
paper \cite{Pauli}, Pauli-forbidden transitions from spacetime noncommutativity
were calculated and confronted with experiments. Here we give details of the
computation missing from this paper. The latter was based on a spacetime
different from the Moyal plane. We argue that it
quantizes time in units of . Energy is then conserved only mod
. Issues related to superselection rules raised by non-Pauli
effects are also discussed in a preliminary manner.Comment: 15 Pages, 1 Table, Full details and further developments of
arXiv:1003.2250. This version is close to the one accepted by JHE
Uniformly Accelerated Observer in Moyal Spacetime
In Minkowski space, an accelerated reference frame may be defined as one that
is related to an inertial frame by a sequence of instantaneous Lorentz
transformations. Such an accelerated observer sees a causal horizon, and the
quantum vacuum of the inertial observer appears thermal to the accelerated
observer, also known as the Unruh effect. We argue that an accelerating frame
may be similarly defined (i.e. as a sequence of instantaneous Lorentz
transformations) in noncommutative Moyal spacetime, and discuss the twisted
quantum field theory appropriate for such an accelerated observer. Our analysis
shows that there are several new features in the case of noncommutative
spacetime: chiral massless fields in dimensions have a qualitatively
different behavior compared to massive fields. In addition, the vacuum of the
inertial observer is no longer an equilibrium thermal state of the accelerating
observer, and the Bose-Einstein distribution acquires -dependent
corrections.Comment: 19 pages. Typos correcte
Quantum Spacetimes in the Year 1
We review certain emergent notions on the nature of spacetime from
noncommutative geometry and their radical implications. These ideas of
spacetime are suggested from developments in fuzzy physics, string theory, and
deformation quantisation. The review focuses on the ideas coming from fuzzy
physics. We find models of quantum spacetime like fuzzy on which states
cannot be localised, but which fluctuate into other manifolds like .
New uncertainty principles concerning such lack of localisability on quantum
spacetimes are formulated.Such investigations show the possibility of
formulating and answering questions like the probabilty of finding a point of a
quantum manifold in a state localised on another one. Additional striking
possibilities indicated by these developments is the (generic) failure of
theorem and the conventional spin-statistics connection. They even suggest that
Planck's `` constant '' may not be a constant, but an operator which does not
commute with all observables. All these novel possibilities arise within the
rules of conventional quantum physics,and with no serious input from gravity
physics.Comment: 11 pages, LaTeX; talks given at Utica and Kolkata .Minor corrections
made and references adde
Unusual Thermodynamics on the Fuzzy 2-Sphere
Higher spin Dirac operators on both the continuum sphere() and its fuzzy
analog() come paired with anticommuting chirality operators. A
consequence of this is seen in the fermion-like spectrum of these operators
which is especially true even for the case of integer-spin Dirac operators.
Motivated by this feature of the spectrum of a spin 1 Dirac operator on
, we assume the spin 1 particles obey Fermi-Dirac statistics. This
choice is inspite of the lack of a well defined spin-statistics relation on a
compact surface such as . The specific heats are computed in the cases of
the spin and spin 1 Dirac operators. Remarkably the specific heat
for a system of spin particles is more than that of the spin 1
case, though the number of degrees of freedom is more in the case of spin 1
particles. The reason for this is inferred through a study of the spectrums of
the Dirac operators in both the cases. The zero modes of the spin 1 Dirac
operator is studied as a function of the cut-off angular momentum and is
found to follow a simple power law. This number is such that the number of
states with positive energy for the spin 1 and spin system become
comparable. Remarks are made about the spectrums of higher spin Dirac operators
as well through a study of their zero-modes and the variation of their spectrum
with degeneracy. The mean energy as a function of temperature is studied in
both the spin and spin 1 cases. They are found to deviate from
the standard ideal gas law in 2+1 dimensions.Comment: 19 pages, 7 figures. The paper has been significantly modified. Main
results are unchange
A projective Dirac operator on CP^2 within fuzzy geometry
We propose an ansatz for the commutative canonical spin_c Dirac operator on
CP^2 in a global geometric approach using the right invariant (left action-)
induced vector fields from SU(3). This ansatz is suitable for noncommutative
generalisation within the framework of fuzzy geometry. Along the way we
identify the physical spinors and construct the canonical spin_c bundle in this
formulation. The chirality operator is also given in two equivalent forms.
Finally, using representation theory we obtain the eigenspinors and calculate
the full spectrum. We use an argument from the fuzzy complex projective space
CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show
that our commutative projected spin_c bundle has the correct
SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos
correcte
Matrix models on the fuzzy sphere
Field theory on a fuzzy noncommutative sphere can be considered as a
particular matrix approximation of field theory on the standard commutative
sphere. We investigate from this point of view the scalar theory. We
demonstrate that the UV/IR mixing problems of this theory are localized to the
tadpole diagrams and can be removed by an appropiate (fuzzy) normal ordering of
the vertex. The perturbative expansion of this theory reduces in the
commutative limit to that on the commutative sphere.Comment: 6 pages, LaTeX2e, Talk given at the NATO Advanced Research Workshop
on Confiment, Topology, and other Non-Perturbative Aspects of QCD, Stara
Lesna, Slovakia, Jan. 21-27, 200
Community composition of nitrous oxide reducing bacteria investigated using a functional gene microarray
The diversity and environmental distribution of the nosZ gene, which encodes the enzyme responsible for the consumption of nitrous oxide, was investigated in marine and terrestrial environments using a functional gene microarray. The microbial communities represented by the nosZ gene probes showed strong biogeographical separation. Communities from surface ocean waters and agricultural soils differed significantly from each other and from those in oceanic oxygen minimum zones. Atypical nosZ genes, usually associated with incomplete denitrification pathways, were detected in all the environments, including surface ocean waters. The abundance of nosZ genes, as estimated by quantitative PCR, was highest in agricultural soils and lowest in surface ocean waters
Phase structure of fuzzy black holes
Noncommutative deformations of the BTZ blackholes are described by
noncommutative cylinders. We study the scalar fields in this background. The
spectrum is studied analytically and through numerical simulations we establish
the existence of novel `stripe phases'. These are different from stripes on
Moyal spaces and stable due to topological obstruction.Comment: 18 pages, 4 figures, minor changes in the tex
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