6,538 research outputs found
Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction
We show that, in a model where a non-relativistic particle is coupled to a
quantized relativistic scalar Bose field, the embedded mass shell of the
particle dissolves in the continuum when the interaction is turned on, provided
the coupling constant is sufficiently small. More precisely, under the
assumption that the fiber eigenvectors corresponding to the putative mass shell
are differentiable as functions of the total momentum of the system, we show
that a mass shell could exist only at a strictly positive distance from the
unperturbed embedded mass shell near the boundary of the energy-momentum
spectrum.Comment: Revised version: a remark added at the end of Section
Magnetism and the Weiss Exchange Field - A Theoretical Analysis Inspired by Recent Experiments
The huge spin precession frequency observed in recent experiments with
spin-polarized beams of hot electrons shot through magnetized films is
interpreted as being caused by Zeeman coupling of the electron spins to the
so-called Weiss exchange field in the film. A "Stern-Gerlach experiment" for
electrons moving through an inhomogeneous exchange field is proposed. The
microscopic origin of exchange interactions and of large mean exchange fields,
leading to different types of magnetic order, is elucidated. A microscopic
derivation of the equations of motion of the Weiss exchange field is presented.
Novel proofs of the existence of phase transitions in quantum XY-models and
antiferromagnets, based on an analysis of the statistical distribution of the
exchange field, are outlined.Comment: 36 pages, 3 figure
Long range order for lattice dipoles
We consider a system of classical Heisenberg spins on a cubic lattice in
dimensions three or more, interacting via the dipole-dipole interaction. We
prove that at low enough temperature the system displays orientational long
range order, as expected by spin wave theory. The proof is based on reflection
positivity methods. In particular, we demonstrate a previously unproven
conjecture on the dispersion relation of the spin waves, first proposed by
Froehlich and Spencer, which allows one to apply infrared bounds for estimating
the long distance behavior of the spin-spin correlation functions.Comment: 9 page
The Chern-Simons Action in Non-Commutative Geometry
A general definition of Chern-Simons actions in non-commutative geometry is
proposed and illustrated in several examples. These are based on
``space-times'' which are products of even-dimensional, Riemannian spin
manifolds by a discrete (two-point) set. If the *algebras of operators
describing the non-commutative spaces are generated by functions over such
``space-times'' with values in certain Clifford algebras the Chern-Simons
actions turn out to be the actions of topological gravity on the
even-dimensional spin manifolds. By contrasting the space of field
configurations in these examples in an appropriate manner one is able to
extract dynamical actions from Chern-Simons actions.Comment: 40 page
KMS, etc
A general form of the ``Wick rotation'', starting from imaginary-time Green
functions of quantum-mechanical systems in thermal equilibrium at positive
temperature, is established. Extending work of H. Araki, the role of the KMS
condition and of an associated anti-unitary symmetry operation, the ``modular
conjugation'', in constructing analytic continuations of Green functions from
real- to imaginary times, and back, is clarified.
The relationship between the KMS condition for the vacuum with respect to
Lorentz boosts, on one hand, and the spin-statistics connection and the PCT
theorem, on the other hand, in local, relativistic quantum field theory is
recalled.
General results on the reconstruction of local quantum theories in various
non-trivial gravitational backgrounds from ``Euclidian amplitudes'' are
presented. In particular, a general form of the KMS condition is proposed and
applied, e.g., to the Unruh- and the Hawking effects.
This paper is dedicated to Huzihiro Araki on the occasion of his seventieth
birthday, with admiration, affection and best wishes.Comment: 56 pages, submitted to J. Math. Phy
Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics
A C*-algebra containing the CCR and CAR algebras as its subalgebras and
naturally described as the semidirect product of these algebras is discussed. A
particular example of this structure is considered as a model for the algebra
of asymptotic fields in quantum electrodynamics, in which Gauss' law is
respected. The appearence in this algebra of a phase variable related to
electromagnetic potential leads to the universal charge quantization.
Translationally covariant representations of this algebra with energy-momentum
spectrum in the future lightcone are investigated. It is shown that vacuum
representations are necessarily nonregular with respect to total
electromagnetic field. However, a class of translationally covariant,
irreducible representations is constructed excplicitly, which remain as close
as possible to the vacuum, but are regular at the same time. The spectrum of
energy-momentum fills the whole future lightcone, but there are no vectors with
energy-momentum lying on a mass hyperboloid or in the origin.Comment: 42 pages, LaTeX; minor corrections, a reference adde
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