5,318 research outputs found
Emergent gauge dynamics of highly frustrated magnets
Condensed matter exhibits a wide variety of exotic emergent phenomena such as
the fractional quantum Hall effect and the low temperature cooperative behavior
of highly frustrated magnets. I consider the classical Hamiltonian dynamics of
spins of the latter phenomena using a method introduced by Dirac in the 1950s
by assuming they are constrained to their lowest energy configurations as a
simplifying measure. Focusing on the kagome antiferromagnet as an example, I
find it is a gauge system with topological dynamics and non-locally connected
edge states for certain open boundary conditions similar to doubled
Chern-Simons electrodynamics expected of a spin liquid. These dynamics
are also similar to electrons in the fractional quantum Hall effect. The
classical theory presented here is a first step towards a controlled
semi-classical description of the spin liquid phases of many pyrochlore and
kagome antiferromagnets and towards a description of the low energy classical
dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and
some additional improvements. 21 pages, 5 figure
A Gauge-Gravity Relation in the One-loop Effective Action
We identify an unusual new gauge-gravity relation: the one-loop effective
action for a massive spinor in 2n dimensional AdS space is expressed in terms
of precisely the same function [a certain multiple gamma function] as the
one-loop effective action for a massive charged scalar in 4n dimensions in a
maximally symmetric background electromagnetic field [one for which the
eigenvalues of F_{\mu\nu} are maximally degenerate, corresponding in 4
dimensions to a self-dual field, equivalently to a field of definite helicity],
subject to the identification F^2 \Lambda, where \Lambda is the
gravitational curvature. Since these effective actions generate the low energy
limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a
nontrivial gauge-gravity relation at the non-perturbative level and at the
amplitude level.Comment: 6 page
Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
We extend our previous results of simplified expressions for functional
determinants for radial Schr\"odinger operators to the computation of vacuum
energy, or mass corrections, for static but spatially radial backgrounds, and
for domain wall configurations. Our method is based on the zeta function
approach to the Gel'fand-Yaglom theorem, suitably extended to higher
dimensional systems on separable manifolds. We find new expressions that are
easy to implement numerically, for both zero and nonzero temperature.Comment: 30 page
The Landau problem and noncommutative quantum mechanics
The conditions under which noncommutative quantum mechanics and the Landau
problem are equivalent theories is explored. If the potential in noncommutative
quantum mechanics is chosen as with defined in the
text, then for the value (that
measures the noncommutative effects of the space), the Landau problem and
noncommutative quantum mechanics are equivalent theories in the lowest Landau
level. For other systems one can find differents values for
and, therefore, the possible bounds for should be searched in
a physical independent scenario. This last fact could explain the differents
bounds for found in the literature.Comment: This a rewritten and corrected version of our previous preprint
hep-th/010517
Functional Determinants in Quantum Field Theory
Functional determinants of differential operators play a prominent role in
theoretical and mathematical physics, and in particular in quantum field
theory. They are, however, difficult to compute in non-trivial cases. For one
dimensional problems, a classical result of Gel'fand and Yaglom dramatically
simplifies the problem so that the functional determinant can be computed
without computing the spectrum of eigenvalues. Here I report recent progress in
extending this approach to higher dimensions (i.e., functional determinants of
partial differential operators), with applications in quantum field theory.Comment: Plenary talk at QTS5 (Quantum Theory and Symmetries); 16 pp, 2 fig
The Physical Projector and Topological Quantum Field Theories: U(1) Chern-Simons Theory in 2+1 Dimensions
The recently proposed physical projector approach to the quantisation of
gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1
dimensions as one of the simplest examples of a topological quantum field
theory. The physical projector is explicitely demonstrated to be capable of
effecting the required projection from the initially infinite number of degrees
of freedom to the finite set of gauge invariant physical states whose
properties are determined by the topology of the underlying manifold.Comment: 24 pages, no figures, plain LaTeX file; one more reference added.
Final version to appear in Jour. Phys.
QED vacuum fluctuations and induced electric dipole moment of the neutron
Quantum fluctuations in the QED vacuum generate non-linear effects, such as
peculiar induced electromagnetic fields. In particular, we show here that an
electrically neutral particle, possessing a magnetic dipole moment, develops an
induced electric dipole-type moment with unusual angular dependence, when
immersed in a quasistatic, constant external electric field. The calculation of
this effect is done in the framework of the Euler-Heisenberg effective QED
Lagrangian, corresponding to the weak field asymptotic expansion of the
effective action to one-loop order. It is argued that the neutron might be a
good candidate to probe this signal of non-linearity in QED.Comment: A misprint has been corrected, and three new references have been
adde
On the QED Effective Action in Time Dependent Electric Backgrounds
We apply the resolvent technique to the computation of the QED effective
action in time dependent electric field backgrounds. The effective action has
both real and imaginary parts, and the imaginary part is related to the pair
production probability in such a background. The resolvent technique has been
applied previously to spatially inhomogeneous magnetic backgrounds, for which
the effective action is real. We explain how dispersion relations connect these
two cases, the magnetic case which is essentially perturbative in nature, and
the electric case where the imaginary part is nonperturbative. Finally, we use
a uniform semiclassical approximation to find an expression for very general
time dependence for the background field. This expression is remarkably similar
in form to Schwinger's classic result for the constant electric background.Comment: 27 pages, no figures; reference adde
Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions
We analyze the large-order behavior of the perturbative weak-field expansion
of the effective Lagrangian density of a massive scalar in de Sitter and anti
de Sitter space, and show that this perturbative information is not sufficient
to describe the non-perturbative behavior of these theories, in contrast to the
analogous situation for the Euler-Heisenberg effective Lagrangian density for
charged scalars in constant electric and magnetic background fields. For
example, in even dimensional de Sitter space there is particle production, but
the effective Lagrangian density is nevertheless real, even though its
weak-field expansion is a divergent non-alternating series whose formal
imaginary part corresponds to the correct particle production rate. This
apparent puzzle is resolved by considering the full non-perturbative structure
of the relevant Feynman propagators, and cannot be resolved solely from the
perturbative expansion.Comment: 18 page
The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
Particle production due to external fields (electric, chromo-electric or
gravitational) requires evolving an initial state through an interaction with a
time-dependent background, with the rate being computed from a Bogoliubov
transformation between the in and out vacua. When the background fields have
temporal profiles with sub-structure, a semiclassical analysis of this problem
confronts the full subtlety of the Stokes phenomenon: WKB solutions are only
local, while the production rate requires global information. Incorporating the
Stokes phenomenon, we give a simple quantitative explanation of the recently
computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of
e+e- pairs produced from vacuum subjected to a time-dependent electric field
with sub-cycle laser pulse structure. This approach also explains naturally why
for spinor and scalar QED these oscillations are out of phase.Comment: 5 pages, 4 figs.; v2 sign typo corrected, version to appear in PR
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