2,814 research outputs found
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
Skyrmions, Spectral Flow and Parity Doubles
It is well-known that the winding number of the Skyrmion can be identified as
the baryon number. We show in this paper that this result can also be
established using the Atiyah-Singer index theorem and spectral flow arguments.
We argue that this proof suggests that there are light quarks moving in the
field of the Skyrmion. We then show that if these light degrees of freedom are
averaged out, the low energy excitations of the Skyrmion are in fact spinorial.
A natural consequence of our approach is the prediction of a state
and its excitations in addition to the nucleon and delta. Using the recent
numerical evidence for the existence of Skyrmions with discrete spatial
symmetries, we further suggest that the the low energy spectrum of many light
nuclei may possess a parity doublet structure arising from a subtle topological
interaction between the slow Skyrmion and the fast quarks. We also present
tentative experimental evidence supporting our arguments.Comment: 22 pages, LaTex. Uses amstex, amssym
Dirac operator on the q-deformed Fuzzy sphere and Its spectrum
The q-deformed fuzzy sphere is the algebra of
dim. matrices, covariant with respect to the adjoint action
of \uq and in the limit , it reduces to the fuzzy sphere
. We construct the Dirac operator on the q-deformed fuzzy
sphere- using the spinor modules of \uq. We explicitly obtain
the zero modes and also calculate the spectrum for this Dirac operator. Using
this Dirac operator, we construct the \uq invariant action for the spinor
fields on which are regularised and have only finite modes. We
analyse the spectrum for both being root of unity and real, showing
interesting features like its novel degeneracy. We also study various limits of
the parameter space (q, N) and recover the known spectrum in both fuzzy and
commutative sphere.Comment: 19 pages, 6 figures, more references adde
Fuzzy Nambu-Goldstone Physics
In spacetime dimensions larger than 2, whenever a global symmetry G is
spontaneously broken to a subgroup H, and G and H are Lie groups, there are
Nambu-Goldstone modes described by fields with values in G/H. In
two-dimensional spacetimes as well, models where fields take values in G/H are
of considerable interest even though in that case there is no spontaneous
breaking of continuous symmetries. We consider such models when the world sheet
is a two-sphere and describe their fuzzy analogues for G=SU(N+1),
H=S(U(N-1)xU(1)) ~ U(N) and G/H=CP^N. More generally our methods give fuzzy
versions of continuum models on S^2 when the target spaces are Grassmannians
and flag manifolds described by (N+1)x(N+1) projectors of rank =< (N+1)/2.
These fuzzy models are finite-dimensional matrix models which nevertheless
retain all the essential continuum topological features like solitonic sectors.
They seem well-suited for numerical work.Comment: Latex, 18 pages; references added, typos correcte
Bosonic Description of Spinning Strings in Dimensions
We write down a general action principle for spinning strings in 2+1
dimensional space-time without introducing Grassmann variables. The action is
written solely in terms of coordinates taking values in the 2+1 Poincare group,
and it has the usual string symmetries, i.e. it is invariant under a)
diffeomorphisms of the world sheet and b) Poincare transformations. The system
can be generalized to an arbitrary number of space-time dimensions, and also to
spinning membranes and p-branes.Comment: Latex, 12 page
Non-Linear Sigma Model on the Fuzzy Supersphere
In this note we develop fuzzy versions of the supersymmetric non-linear sigma
model on the supersphere S^(2,2). In hep-th/0212133 Bott projectors have been
used to obtain the fuzzy CP^1 model. Our approach utilizes the use of
supersymmetric extensions of these projectors. Here we obtain these (super)
-projectors and quantize them in a fashion similar to the one given in
hep-th/0212133. We discuss the interpretation of the resulting model as a
finite dimensional matrix model.Comment: 11 pages, LaTeX, corrected typo
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
Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics
Time-space noncommutativity leads to quantisation of time and energy
nonconservation when time is conjugate to a compact spatial direction like a
circle. In this context energy is conserved only modulo some fixed unit. Such a
possibility arises for example in theories with a compact extra dimension with
which time does not commute. The above results suggest striking
phenomenological consequences in extra dimensional theories and elsewhere. In
this paper we develop scattering theory for discrete time translations. It
enables the calculation of transition probabilities for energy nonconserving
processes and has a central role both in formal theory and phenomenology.
We can also consider space-space noncommutativity where one of the spatial
directions is a circle. That leads to the quantisation of the remaining spatial
direction and conservation of momentum in that direction only modulo some fixed
unit, as a simple adaptation of the results in this paper shows.Comment: 17 pages, LaTex; minor correction
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