2,029 research outputs found

### 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 $\theta_{\mu\nu}$. 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 $\gtrsim 10^{24}\textrm{TeV}$. 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

### 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

### Gauge Symmetries,Topology and Quantisation

The following two loosely connected sets of topics are reviewed in these
lecture notes: 1) Gauge invariance, its treatment in field theories and its
implications for internal symmetries and edge states such as those in the
quantum Hall effect. 2) Quantisation on multiply connected spaces and a
topological proof the spin-statistics theorem which avoids quantum field theory
and relativity. Under 1), after explaining the meaning of gauge invariance and
the theory of constraints, we discuss boundary conditions on gauge
transformations and the definition of internal symmetries in gauge field
theories. We then show how the edge states in the quantum Hall effect can be
derived from the Chern-Simons action using the preceding ideas. Under 2), after
explaining the significance of fibre bundles for quantum physics, we review
quantisation on multiply connected spaces in detail, explaining also
mathematical ideas such as those of the universal covering space and the
fundamental group. These ideas are then used to prove the aforementioned
topological spin-statistics theorem.e of the universal covering space and the
fundamental group.Comment: 74pages (Lectures

### 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 $(1/2)^{-}$ 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

### 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 $S^4$ on which states
cannot be localised, but which fluctuate into other manifolds like $CP^3$ .
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 $CPT$
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

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