136 research outputs found
The Quest for Understanding in Relativistic Quantum Physics
We discuss the status and some perspectives of relativistic quantum physics.Comment: Invited contribution to the Special Issue 2000 of the Journal of
Mathematical Physics, 38 pages, typos corrected and references added, as to
appear in JM
Linear Connections in Non-Commutative Geometry
A construction is proposed for linear connections on non-commutative
algebras. The construction relies on a generalisation of the Leibnitz rules of
commutative geometry and uses the bimodule structure of . A special
role is played by the extension to the framework of non-commutative geometry of
the permutation of two copies of . The construction of the linear
connection as well as the definition of torsion and curvature is first proposed
in the setting of the derivations based differential calculus of Dubois-
Violette and then a generalisation to the framework proposed by Connes as well
as other non-commutative differential calculi is suggested. The covariant
derivative obtained admits an extension to the tensor product of several copies
of . These constructions are illustrated with the example of the
algebra of matrices.Comment: 15 pages, LMPM ../94 (uses phyzzx
How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential
The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system
New Concepts in Particle Physics from Solution of an Old Problem
Recent ideas on modular localization in local quantum physics are used to
clarify the relation between on- and off-shell quantities in particle physics;
in particular the relation between on-shell crossing symmetry and off-shell
Einstein causality. Among the collateral results of this new nonperturbative
approach are profound relations between crossing symmetry of particle physics
and Hawking-Unruh like thermal aspects (KMS property, entropy attached to
horizons) of quantum matter behind causal horizons, aspects which hitherto were
exclusively related with Killing horizons in curved spacetime rather than with
localization aspects in Minkowski space particle physics. The scope of this
modular framework is amazingly wide and ranges from providing a conceptual
basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models
to a decomposition theory of QFT's in terms of a finite collection of unitarily
equivalent chiral conformal theories placed a specified relative position
within a common Hilbert space (in d=1+1 a holographic relation and in higher
dimensions more like a scanning). The new framework gives a spacetime
interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal
aspects.Comment: In this form it will appear in JPA Math Gen, 47 pages tcilate
Anomalous Scale Dimensions from Timelike Braiding
Using the previously gained insight about the particle/field relation in
conformal quantum field theories which required interactions to be related to
the existence of particle-like states associated with fields of anomalous
scaling dimensions, we set out to construct a classification theory for the
spectra of anomalous dimensions. Starting from the old observations on
conformal superselection sectors related to the anomalous dimensions via the
phases which appear in the spectral decomposition of the center of the
conformal covering group we explore the possibility
of a timelike braiding structure consistent with the timelike ordering which
refines and explains the central decomposition. We regard this as a preparatory
step in a new construction attempt of interacting conformal quantum field
theories in D=4 spacetime dimensions. Other ideas of constructions based on the
- or the perturbative SYM approach in their relation to the
present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages
tcilatex, 3 latexcad figure
Pauli problem for a spin of arbitrary length: A simple method to determine its wave function
The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems
The Pivotal Role of Causality in Local Quantum Physics
In this article an attempt is made to present very recent conceptual and
computational developments in QFT as new manifestations of old and well
establihed physical principles. The vehicle for converting the
quantum-algebraic aspects of local quantum physics into more classical
geometric structures is the modular theory of Tomita. As the above named
laureate to whom I have dedicated has shown together with his collaborator for
the first time in sufficient generality, its use in physics goes through
Einstein causality. This line of research recently gained momentum when it was
realized that it is not only of structural and conceptual innovative power (see
section 4), but also promises to be a new computational road into
nonperturbative QFT (section 5) which, picturesquely speaking, enters the
subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of
Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik
FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud
150, 22290-180 Rio de Janeiro, Brazi
Responsive glyco-poly(2-oxazoline)s: synthesis, cloud point tuning, and lectin binding
A new sugar-substituted 2-oxazoline monomer was prepared using the copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction. Its copolymerization with 2-ethyl-2-oxazoline as well as 2-(dec-9-enyl)-2-oxazoline, yielding well-defined copolymers with the possibility to tune the properties by thiol-ene "click" reactions, is described. Extensive solubility studies on the corresponding glycocopolymers demonstrated that the lower critical solution temperature behavior and pH-responsiveness of these copolymers can be adjusted in water and phosphate-buffered saline (PBS) depending on the choice of the thiol. By conjugation of 2,3,4,6-tetra-O-acetyl-1-thio-beta-D-glucopyranose and subsequent deprotection of the sugar moieties, the hydrophilicity of the copolymer could be increased significantly, allowing a cloud-point tuning in the physiological range. Furthermore, the binding capability of the glycosylated copoly(2-oxazoline) to concanavalin A was investigated
A New Approach to Spin and Statistics
We give an algebraic proof of the spin-statistics connection for the
parabosonic and parafermionic quantum topological charges of a theory of local
observables with a modular PCT-symmetry. The argument avoids the use of the
spinor calculus and also works in 1+2 dimensions. It is expected to be a
progress towards a general spin-statistics theorem including also
(1+2)-dimensional theories with braid group statistics.Comment: LATEX, 15 pages, no figure
Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?
The question of what it means for a theory to describe the same physics on
all spacetimes (SPASs) is discussed. As there may be many answers to this
question, we isolate a necessary condition, the SPASs property, that should be
satisfied by any reasonable notion of SPASs. This requires that if two theories
conform to a common notion of SPASs, with one a subtheory of the other, and are
isomorphic in some particular spacetime, then they should be isomorphic in all
globally hyperbolic spacetimes (of given dimension). The SPASs property is
formulated in a functorial setting broad enough to describe general physical
theories describing processes in spacetime, subject to very minimal
assumptions. By explicit constructions, the full class of locally covariant
theories is shown not to satisfy the SPASs property, establishing that there is
no notion of SPASs encompassing all such theories. It is also shown that all
locally covariant theories obeying the time-slice property possess two local
substructures, one kinematical (obtained directly from the functorial
structure) and the other dynamical (obtained from a natural form of dynamics,
termed relative Cauchy evolution). The covariance properties of relative Cauchy
evolution and the kinematic and dynamical substructures are analyzed in detail.
Calling local covariant theories dynamically local if their kinematical and
dynamical local substructures coincide, it is shown that the class of
dynamically local theories fulfills the SPASs property. As an application in
quantum field theory, we give a model independent proof of the impossibility of
making a covariant choice of preferred state in all spacetimes, for theories
obeying dynamical locality together with typical assumptions.Comment: 60 pages, LaTeX. Version to appear in Annales Henri Poincar
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