3,323 research outputs found
Bosonization and Current Algebra of Spinning Strings
We write down a general geometric action principle for spinning strings in
-dimensional Minkowski space, which is formulated without the use of
Grassmann coordinates. Instead, it is constructed in terms of the pull-back of
a left invariant Maurer-Cartan form on the -dimensional Poincar\'e group to
the world sheet. The system contains some interesting special cases. Among them
are the Nambu string (as well as, null and tachyionic strings) where the spin
vanishes, and also the case of a string with a spin current - but no momentum
current. We find the general form for the Virasoro generators, and show that
they are first class constraints in the Hamiltonian formulation of the theory.
The current algebra associated with the momentum and angular momentum densities
are shown, in general, to contain rather complicated anomaly terms which
obstruct quantization. As expected, the anomalies vanish when one specializes
to the case of the Nambu string, and there one simply recovers the algebra
associated with the Poincar\'e loop group. We speculate that there exist other
cases where the anomalies vanish, and that these cases give the bosonization of
the known pseudoclassical formulations of spinning strings.Comment: Latex file, 29 p
Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR Mixing
In the absence of gauge fields, quantum field theories on the
Groenewold-Moyal (GM) plane are invariant under a twisted action of the
Poincare group if they are formulated following [1, 2, 3, 4, 5, 6]. In that
formulation, such theories also have no UV-IR mixing [7]. Here we investigate
UV-IR mixing in gauge theories with matter following the approach of [3, 4]. We
prove that there is UV-IR mixing in the one-loop diagram of the S-matrix
involving a coupling between gauge and matter fields on the GM plane, the gauge
field being nonabelian. There is no UV-IR mixing if it is abelian.Comment: 11 pages, 3 figure
Non-Pauli Transitions From Spacetime Noncommutativity
There are good reasons to suspect that spacetime at Planck scales is
noncommutative. Typically this noncommutativity is controlled by fixed
"vectors" or "tensors" with numerical entries. For the Moyal spacetime, it is
the antisymmetric matrix . In approaches enforcing Poincar\'e
invariance, these deform or twist the method of (anti-)symmetrization of
identical particle state vectors. We argue that the earth's rotation and
movements in the cosmos are "sudden" events to Pauli-forbidden processes. They
induce (twisted) bosonic components in state vectors of identical spinorial
particles in the presence of a twist. These components induce non-Pauli
transitions. From known limits on such transitions, we infer that the energy
scale for noncommutativity is . This suggests a
new energy scale beyond Planck scale.Comment: 11 pages, 1 table, Slightly revised for clarity
Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple
Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with
the group SU(2) in this manner. They are useful for regularizing quantum field
theories and modeling spacetimes by non-commutative manifolds. We show that
fuzzy spaces are Hopf algebras and in fact have more structure than the latter.
They are thus candidates for quantum symmetries. Using their generalized Hopf
algebraic structures, we can also model processes where one fuzzy space splits
into several fuzzy spaces. For example we can discuss the quantum transition
where the fuzzy sphere for angular momentum J splits into fuzzy spheres for
angular momenta K and L.Comment: LaTeX, 13 pages, v3: minor additions, added references, v4: corrected
typos, to appear in IJMP
Duality in Fuzzy Sigma Models
Nonlinear `sigma' models in two dimensions have BPS solitons which are
solutions of self- and anti-self-duality constraints. In this paper, we find
their analogues for fuzzy sigma models on fuzzy spheres which were treated in
detail by us in earlier work. We show that fuzzy BPS solitons are quantized
versions of `Bott projectors', and construct them explicitly. Their
supersymmetric versions follow from the work of S. Kurkcuoglu.Comment: Latex, 9 pages; misprints correcte
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
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
Bringing Up a Quantum Baby
Any two infinite-dimensional (separable) Hilbert spaces are unitarily
isomorphic. The sets of all their self-adjoint operators are also therefore
unitarily equivalent. Thus if all self-adjoint operators can be observed, and
if there is no further major axiom in quantum physics than those formulated for
example in Dirac's `Quantum Mechanics', then a quantum physicist would not be
able to tell a torus from a hole in the ground. We argue that there are indeed
such axioms involving vectors in the domain of the Hamiltonian: The
``probability densities'' (hermitean forms) \psi^\dagger \chi for \psi,\chi in
this domain generate an algebra from which the classical configuration space
with its topology (and with further refinements of the axiom, its C^K and
C^infinity structures) can be reconstructed using Gel'fand - Naimark theory.
Classical topology is an attribute of only certain quantum states for these
axioms, the configuration space emergent from quantum physics getting
progressively less differentiable with increasingly higher excitations of
energy and eventually altogether ceasing to exist. After formulating these
axioms, we apply them to show the possibility of topology change and to discuss
quantized fuzzy topologies. Fundamental issues concerning the role of time in
quantum physics are also addressed.Comment: 23 pages, 2 figures ( ref. updated, no other changes
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