160 research outputs found
Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions
Recently, motivated by certain loop quantum gravity inspired corrections, it
was shown that for spherically symmetric midisuperspace models infinitely many
second derivative theories of gravity exist (as revealed by the presence of
three arbitrary functions in the corresponding Lagrangian/Hamiltonian) and not
just those allowed by spherically symmetric general relativity. This freedom
can be interpreted as the freedom to accommodate certain quantum gravity
corrections in these models even in the absence of higher curvature terms (at a
semi-classical level, at least). For a particular choice of the arbitrary
functions it is shown that the new theories map to spherically symmetric
general relativity in arbitrary number of (integer) dimensions thus explicitly
demonstrating that when working with midisuperspace models, one loses the
information about the dimensionality of the full spacetime. In addition, it is
shown that these new theories can accommodate scenarios of fractional spacetime
dimensions as well as those of emergent spacetime dimensions -- a possibility
suggested by various approaches to quantum gravity.Comment: 10 page
Fermionic edge states and new physics
We investigate the properties of the Dirac operator on manifolds with
boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact
counting of the number of edge states for boundaries with isometry of a sphere
is given. We show that the problem with the above boundary condition can be
mapped to one where the manifold is extended beyond the boundary and the
boundary condition is replaced by a delta function potential of suitable
strength. We also briefly highlight how the problem of the self-adjointness of
the operators in the presence of moving boundaries can be simplified by
suitable transformations which render the boundary fixed and modify the
Hamiltonian and the boundary condition to reflect the effect of moving
boundary.Comment: 24 pages, 3 figures. Title changed, additional material in the
Introduction section, the Application section and in the Discussion section
highlighting some recent work on singular potentials, several references
added. Conclusions remain unchanged. Version matches the version to appear in
PR
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