999 research outputs found
Axiomatic Holonomy Maps and Generalized Yang-Mills Moduli Space
This article is a follow-up of ``Holonomy and Path Structures in General
Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30,
No.9, 1991). Its main goal is to provide an alternative proof of this part of
the reconstruction theorem which concerns the existence of a connection. A
construction of connection 1-form is presented. The formula expressing the
local coefficients of connection in terms of the holonomy map is obtained as an
immediate consequence of that construction. Thus the derived formula coincides
with that used in "On Loop Space Formulation of Gauge Theories" by Chan, H.-M.,
Scharbach, P. and Tsou S.T. (Ann.Phys., vol.167, 454-472, 1986). The
reconstruction and representation theorems form a generalization of the fact
that the pointed configuration space of the classical Yang-Mills theory is
equivalent to the set of all holonomy maps. The point of this generalization is
that there is a one-to-one correspondence not only between the holonomy maps
and the orbits in the space of connections, but also between all maps from the
loop space on to group fulfilling some axioms and all possible
equivalence classes of bundles with connection, where the equivalence
relation is defined by bundle isomorphism in a natural way.Comment: amslatex, 7 pages, no figure
Classical and Quantum Interaction of the Dipole
A unified and fully relativistic treatment of the interaction of the electric
and magnetic dipole moments of a particle with the electromagnetic field is
given. New forces on the particle due to the combined effect of electric and
magnetic dipoles are obtained. Four new experiments are proposed, three of
which would observe topological phase shifts.Comment: 10 pages, Latex/Revtex. Some minor errors have been correcte
Coherent States and Duality
We formulate a relation between quantum-mechanical coherent states and
complex-differentiable structures on the classical phase space of a
finite number of degrees of freedom. Locally-defined coherent states
parametrised by the points of exist when there is an almost complex
structure on . When admits a complex structure, such
coherent states are globally defined on . The picture of quantum
mechanics that emerges allows to implement duality transformations.Comment: 7 pages, LaTe
Quantum Interference to Measure Spacetime Curvature: A Proposed Experiment at the Intersection of Quantum Mechanics and General Relativity
An experiment in Low Earth Orbit (LEO) is proposed to measure components of
the Riemann curvature tensor using atom interferometry. We show that the
difference in the quantum phase of an atom that can travel along
two intersecting geodesics is given by times the spacetime
volume contained within the geodesics. Our expression for also
holds for gravitational waves in the long wavelength limit.Comment: 7 pages LaTeXed with RevTeX 4.0, 2 figures. Submitted to the 2003
Gravity Research Foundation Essay Contes
Action based approach to the dynamics of extended bodies in General Relativity
We present, for the first time, an action principle that gives the equations
of motion of an extended body possessing multipole moments in an external
gravitational field, in the weak field limit. From the action, the
experimentally observable quantum phase shifts in the wavefunction of an
extended object due to the coupling of its multipole moments with the
gravitational field are obtained. Also, since the theory may be quantized using
the action, the present approach is useful in the interface between general
relativity and quantum mechanics.Comment: This essay received an ``honorable mention'' in the 2003 Gravity
Research Foundation essay competitio
Islands around Gulf of Mannar
Island is a body of land smaller than a continent and surrounded by watet. There are about 21 islands in Gulf ofMannar on the South eastern coast of India extending from Rameswaram island on the north and Tuticorin on the south between latitudeS' 50' -9' 15' N and longtitude 78' 13' - 79 '14' E
Topology, Locality, and Aharonov-Bohm Effect with Neutrons
Recent neutron interferometry experiments have been interpreted as
demonstrating a new topological phenomenon similar in principle to the usual
Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the
electron's charge. We show that the new phenomenon, called Scalar AB (SAB)
effect, follows from an ordinary local interaction, contrary to the usual AB
effect, and we argue that the SAB effect is not a topological effect by any
useful definition. We find that SAB actually measures an apparently novel spin
autocorrelation whose operator equations of motion contain the local torque in
the magnetic field. We note that the same remarks apply to the Aharonov-Casher
effect.Comment: 9 page
Berry phase in a non-isolated system
We investigate the effect of the environment on a Berry phase measurement
involving a spin-half. We model the spin+environment using a biased spin-boson
Hamiltonian with a time-dependent magnetic field. We find that, contrary to
naive expectations, the Berry phase acquired by the spin can be observed, but
only on timescales which are neither too short nor very long. However this
Berry phase is not the same as for the isolated spin-half. It does not have a
simple geometric interpretation in terms of the adiabatic evolution of either
bare spin-states or the dressed spin-resonances that remain once we have traced
out the environment. This result is crucial for proposed Berry phase
measurements in superconducting nanocircuits as dissipation there is known to
be significant.Comment: 4 pages (revTeX4) 2 fig. This version has MAJOR changes to equation
Gravity and Geometric Phases
The behavior of a quantum test particle satisfying the Klein-Gordon equation
in a certain class of 4 dimensional stationary space-times is examined. In a
space-time of a spinning cosmic string, the wave function of a particle in a
box is shown to acquire a geometric phase when the box is transported around a
closed path surrounding the string. When interpreted as an Aharonov-Anandan
geometric phase, the effect is shown to be related to the Aharonov-Bohm effect.Comment: 11 pages, latex fil
Action principle formulation for motion of extended bodies in General Relativity
We present an action principle formulation for the study of motion of an
extended body in General Relativity in the limit of weak gravitational field.
This gives the classical equations of motion for multipole moments of arbitrary
order coupling to the gravitational field. In particular, a new force due to
the octupole moment is obtained. The action also yields the gravitationally
induced phase shifts in quantum interference experiments due to the coupling of
all multipole moments.Comment: Revised version derives Octupole moment force. Some clarifications
and a reference added. To appear in Phys. Rev.
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