4,489 research outputs found
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
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
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
Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties
We study the infrared problem in the usual model of QED with non-relativistic
matter. We prove spectral and regularity properties characterizing the mass
shell of an electron and one-electron infraparticle states of this model. Our
results are crucial for the construction of infraparticle scattering states,
which are treated in a separate paper.Comment: AMS Latex, 45 pages, 2 figure
Representation Theory of Lattice Current Algebras
Lattice current algebras were introduced as a regularization of the left- and
right moving degrees of freedom in the WZNW model. They provide examples of
lattice theories with a local quantum symmetry U_q(\sg). Their representation
theory is studied in detail. In particular, we construct all irreducible
representations along with a lattice analogue of the fusion product for
representations of the lattice current algebra. It is shown that for an
arbitrary number of lattice sites, the representation categories of the lattice
current algebras agree with their continuum counterparts.Comment: 35 pages, LaTeX file, the revised version of the paper, to be
published in Commun. Math. Phys. , the definition of the fusion product for
lattice current algebras is correcte
Spin - or, actually: Spin and Quantum Statistics
The history of the discovery of electron spin and the Pauli principle and the
mathematics of spin and quantum statistics are reviewed. Pauli's theory of the
spinning electron and some of its many applications in mathematics and physics
are considered in more detail. The role of the fact that the tree-level
gyromagnetic factor of the electron has the value g = 2 in an analysis of
stability (and instability) of matter in arbitrary external magnetic fields is
highlighted. Radiative corrections and precision measurements of g are
reviewed. The general connection between spin and statistics, the CPT theorem
and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin
Orbital ordering in transition-metal compounds: I. The 120-degree model
We study the classical version of the 120-degree model. This is an attractive
nearest-neighbor system in three dimensions with XY (rotor) spins and
interaction such that only a particular projection of the spins gets coupled in
each coordinate direction. Although the Hamiltonian has only discrete
symmetries, it turns out that every constant field is a ground state. Employing
a combination of spin-wave and contour arguments we establish the existence of
long-range order at low temperatures. This suggests a mechanism for a type of
ordering in certain models of transition-metal compounds where the very
existence of long-range order has heretofore been a matter of some controversy.Comment: 40 pages, 1 eps fig; a revised version correcting a bunch of small
error
Stochastically positive structures on Weyl algebras. The case of quasi-free states
We consider quasi-free stochastically positive ground and thermal states on
Weyl algebras in Euclidean time formulation. In particular, we obtain a new
derivation of a general form of thermal quasi-free state and give conditions
when such state is stochastically positive i.e. when it defines periodic
stochastic process with respect to Euclidean time, so called thermal process.
Then we show that thermal process completely determines modular structure
canonically associated with quasi-free state on Weyl algebra. We discuss a
variety of examples connected with free field theories on globally hyperbolic
stationary space-times and models of quantum statistical mechanics.Comment: 46 pages, amste
Cosmic Strings on the Lattice
We develop a formalism for the quantization of topologically stable
excitations in the 4-dimensional abelian lattice gauge theory. The excitations
are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The
operators of creation and annihilation of string states are constructed; the
string Green functions are represented as a path integral over random surfaces.
Topological excitations play an important role in the early universe. In the
broken symmetry phase of the spin model, closed global cosmic strings
arise, while in the Higgs phase of the noncompact gauge-Higgs model, local
cosmic strings are present. The compact gauge-Higgs model also involves
monopoles. Then the strings can break if their ends are capped by monopoles.
The topology of the Euclidean string world sheets are studied by numerical
simulations.Comment: 4 pages LaTex (espcrc2.sty), LATTICE'92 contribution, ITEP(1992
On the semiclassical limit of 4d spin foam models
We study the semiclassical properties of the Riemannian spin foam models with
Immirzi parameter that are constructed via coherent states. We show that in the
semiclassical limit the quantum spin foam amplitudes of an arbitrary
triangulation are exponentially suppressed, if the face spins do not correspond
to a discrete geometry. When they do arise from a geometry, the amplitudes
reduce to the exponential of i times the Regge action. Remarkably, the
dependence on the Immirzi parameter disappears in this limit.Comment: 32 pages, 5 figure
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