2,139 research outputs found
Quantum mechanics on manifolds and topological effects
A unique classification of the topological effects associated to quantum
mechanics on manifolds is obtained on the basis of the invariance under
diffeomorphisms and the realization of the Lie-Rinehart relations between the
generators of the diffeomorphism group and the algebra of infinitely
differentiable functions on the manifold. This leads to a unique
("Lie-Rinehart") C* algebra as observable algebra; its regular representations
are shown to be locally Schroedinger and in one to one correspondence with the
unitary representations of the fundamental group of the manifold. Therefore, in
the absence of spin degrees of freedom and external fields, the first homotopy
group of the manifold appears as the only source of topological effects.Comment: A few comments have been added to the Introduction, together with
related references; a few words have been changed in the Abstract and a Note
added to the Titl
Perturbative Quantum Field Theory at Positive Temperatures: An Axiomatic Approach
It is shown that the perturbative expansions of the correlation functions of
a relativistic quantum field theory at finite temperature are uniquely
determined by the equations of motion and standard axiomatic requirements,
including the KMS condition. An explicit expression as a sum over generalized
Feynman graphs is derived. The canonical formalism is not used, and the
derivation proceeds from the beginning in the thermodynamic limit. No doubling
of fields is invoked. An unsolved problem concerning existence of these
perturbative expressions is pointed out.Comment: 17pages Late
IceCube's In-Ice Radio Extension: Status and Results
In 2006-2010, several Radio Frequency (RF) detectors and calibration
equipment were deployed as part of the IceCube array at depths between 5 to
1400 meters in preparation for a future large scale GZK neutrino detector.
IceCube's deep holes and well-established data handling system provide a unique
opportunity for deep-ice RF detection studies at the South-Pole. We will
present verification and calibration results as well as a status-review of
ongoing analyses such as ice-properties, RF noise and reconstruction
algorithms.Comment: 4 pages, 6 figures, to appear in the proceedings of the Acoustic and
Radio EeV Neutrino detection Activities (ARENA) 2010 conferenc
Semiclassical states for quantum cosmology
In a metric variable based Hamiltonian quantization, we give a prescription
for constructing semiclassical matter-geometry states for homogeneous and
isotropic cosmological models. These "collective" states arise as infinite
linear combinations of fundamental excitations in an unconventional "polymer"
quantization. They satisfy a number of properties characteristic of
semiclassicality, such as peaking on classical phase space configurations. We
describe how these states can be used to determine quantum corrections to the
classical evolution equations, and to compute the initial state of the universe
by a backward time evolution.Comment: 13 page
Unstable states in QED of strong magnetic fields
We question the use of stable asymptotic scattering states in QED of strong
magnetic fields. To correctly describe excited Landau states and photons above
the pair creation threshold the asymptotic fields are chosen as generalized
Licht fields. In this way the off-shell behavior of unstable particles is
automatically taken into account, and the resonant divergences that occur in
scattering cross sections in the presence of a strong external magnetic field
are avoided. While in a limiting case the conventional electron propagator with
Breit-Wigner form is obtained, in this formalism it is also possible to
calculate -matrix elements with external unstable particles.Comment: Revtex, 7 pages. To appear in Phys. Rev. D53(2
High-order harmonic generation by static coherent states method in single-electron atomic and molecular systems
We solve the time-dependent Schrodinger equation using the coherent states as basis sets for computing high harmonic generation (HHG) in a full-dimensional single-electron "realistic" system. We apply the static coherent states (SCS) method to investigate HHG in the hydrogen molecular ion induced by a linearly polarized laser field. We show that SCS gives reasonable agreement compared to the three dimensional unitary split-operator approach. Next, we study isolated attosecond pulse generation in H2+. To do so, we employ the well-known polarization gating technique, which combines two delayed counter-rotating circular laser pulses, and opens up a gate at the central portion of the superposed pulse. Our results suggest that the SCS method can be used for full-dimensional quantum simulation of higher dimensional systems such as the hydrogen molecule in the presence of an external laser field
Finite Size Effects in Thermal Field Theory
We consider a neutral self-interacting massive scalar field defined in a
d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the
one-loop perturbative renormalization of this theory in the presence of rigid
boundary surfaces (two parallel hyperplanes), which break translational
symmetry. In order to identify the singular parts of the one-loop two-point and
four-point Schwinger functions, we use a combination of dimensional and
zeta-function analytic regularization procedures. The infinities which occur in
both the regularized one-loop two-point and four-point Schwinger functions fall
into two distinct classes: local divergences that could be renormalized with
the introduction of the usual bulk counterterms, and surface divergences that
demand countertems concentrated on the boundaries. We present the detailed form
of the surface divergences and discuss different strategies that one can assume
to solve the problem of the surface divergences. We also briefly mention how to
overcome the difficulties generated by infrared divergences in the case of
Neumann-Neumann boundary conditions.Comment: 31 pages, latex, to appear in J. Math. Phy
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