1,299 research outputs found
Quantum Geons and Noncommutative Spacetimes
Physical considerations strongly indicate that spacetime at Planck scales is
noncommutative. A popular model for such a spacetime is the Moyal plane. The
Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the
latter is not appropriate for more complicated spacetimes such as those
containing the Friedman-Sorkin (topological) geons. They have rich
diffeomorphism groups and in particular mapping class groups, so that the
statistics groups for N identical geons is strikingly different from the
permutation group . We generalise the Drinfel'd twist to (essentially)
generic groups including to finite and discrete ones and use it to modify the
commutative spacetime algebras of geons as well to noncommutative algebras. The
latter support twisted actions of diffeos of geon spacetimes and associated
twisted statistics. The notion of covariant fields for geons is formulated and
their twisted versions are constructed from their untwisted versions.
Non-associative spacetime algebras arise naturally in our analysis. Physical
consequences, such as the violation of Pauli principle, seem to be the outcomes
of such nonassociativity.
The richness of the statistics groups of identical geons comes from the
nontrivial fundamental groups of their spatial slices. As discussed long ago,
extended objects like rings and D-branes also have similar rich fundamental
groups. This work is recalled and its relevance to the present quantum geon
context is pointed out.Comment: 41 page
Novel Studies on the \eta' Effective Lagrangian
The effective Lagrangian for \eta' incorporating the effect of the QCD
\theta-angle has been developed previously. We revisit this Lagrangian and
carry out its canonical quantization with particular attention to the test
function spaces of constraints and the topology of the \eta'-field. In this
way, we discover a new chirally symmetric coupling of this field to chiral
multiplets which involves in particular fermions. This coupling violates P and
T symmetries. In a subsequent paper, we will evaluate its contribution to the
electric dipole moment (EDM) of fermions. Our motivation is to test whether the
use of mixed states restores P and T invariance, so that EDM vanishes. This
calculation will be shown to have striking new physical consequences.Comment: 14 pages, 1 figure; V2: NEW TITLE; revised version to be published in
JHEP; references adde
Conformal invariance in 2-dimensional discrete field theory
A discretized massless wave equation in two dimensions, on an appropriately
chosen square lattice, exactly reproduces the solutions of the corresponding
continuous equations. We show that the reason for this exact solution property
is the discrete analog of conformal invariance present in the model, and find
more general field theories on a two-dimensional lattice that exactly solve
their continuous limit equations. These theories describe in general
non-linearly coupled bosonic and fermionic fields and are similar to the
Wess-Zumino-Witten model.Comment: 18 pages, RevTeX, 2 figures included; revision of title and
introductio
Generalized Bohr-Sommerfeld rules for anomalies with applications to symmetry breakdown and decoupling
In the presence of anomalies, the requirement that a classical symmetry group G has a proper action on the fermion measure or in the effective Lagrangian description imposes Bohr-Sommerfeld conditions on the anomalies, and often implies that G is broken to a subgroup H as well. We show these results in this paper and apply them to QCD and SU(5). In particular, constraints on the QCD order parameter are derived, and an argument is presented which suggests that the breakdown of the chiral flavor symmetry and the emergence of some sort of generation structure in QCD may be natural
Scalar Field Theory on Fuzzy S^4
Scalar fields are studied on fuzzy and a solution is found for the
elimination of the unwanted degrees of freedom that occur in the model. The
resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4
in the fuzzy context.Comment: 16 pages, LaTe
Interactions of a String Inspired Graviton Field
We continue to explore the possibility that the graviton in two dimensions is
related to a quadratic differential that appears in the anomalous contribution
of the gravitational effective action for chiral fermions. A higher dimensional
analogue of this field might exist as well. We improve the defining action for
this diffeomorphism tensor field and establish a principle for how it interacts
with other fields and with point particles in any dimension. All interactions
are related to the action of the diffeomorphism group. We discuss possible
interpretations of this field.Comment: 12 pages, more readable, references adde
The Fuzzy Disc
We introduce a finite dimensional matrix model approximation to the algebra
of functions on a disc based on noncommutative geometry. The algebra is a
subalgebra of the one characterizing the noncommutative plane with a * product
and depends on two parameters N and theta. It is composed of functions which
decay exponentially outside a disc. In the limit in which the size of the
matrices goes to infinity and the noncommutativity parameter goes to zero the
disc becomes sharper. We introduce a Laplacian defined on the whole algebra and
calculate its eigenvalues. We also calculate the two--points correlation
function for a free massless theory (Green's function). In both cases the
agreement with the exact result on the disc is very good already for relatively
small matrices. This opens up the possibility for the study of field theories
on the disc with nonperturbative methods. The model contains edge states, a
fact studied in a similar matrix model independently introduced by
Balachandran, Gupta and Kurkcuoglu.Comment: 17 pages, 8 figures, references added and correcte
Boundary degrees of freedom in fractional quantum Hall effect: Excitations on common boundary of two samples
Using the Carlip's method we have derived the boundary action for the fermion
Chern-Simons theory of quantum Hall effects on a planar region with a boundary.
We have computed both the bulk and edge responses of currents to the external
electric field. From this we obtain the well-known anomaly relation and the
boundary Hall current without introducing any ad hoc assumptions such as the
chirality condition. In addition, the edge current on the common boundary of
two samples is found to be proportional to the difference between Chern-Simons
coupling strengths.Comment: 20 pages, uses revte
Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator
It is shown that the local axial anomaly in dimensions emerges naturally
if one postulates an underlying noncommutative fuzzy structure of spacetime .
In particular the Dirac-Ginsparg-Wilson relation on is shown to
contain an edge effect which corresponds precisely to the ``fuzzy''
axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant
expansion of the quark propagator in the form where
is the lattice spacing on , is
the covariant noncommutative chirality and is an effective
Dirac operator which has essentially the same IR spectrum as
but differes from it on the UV modes. Most remarkably is the fact that both
operators share the same limit and thus the above covariant expansion is not
available in the continuum theory . The first bit in this expansion
although it vanishes as it stands in the continuum
limit, its contribution to the anomaly is exactly the canonical theta term. The
contribution of the propagator is on the other hand
equal to the toplogical Chern-Simons action which in two dimensions vanishes
identically .Comment: 26 pages, latex fil
Modified Partition Functions, Consistent Anomalies and Consistent Schwinger Terms
A gauge invariant partition function is defined for gauge theories which
leads to the standard quantization. It is shown that the descent equations and
consequently the consistent anomalies and Schwinger terms can be extracted from
this modified partition function naturally.Comment: 25 page
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