11 research outputs found
Renormalization group analysis of the QCD quark potential to order v^2
A one-loop renormalization group analysis of the order v^2 relativistic
corrections to the static QCD potential is presented. The velocity
renormalization group is used to simultaneously sum ln(m/mv) and ln(m/mv^2)
terms. The results are compared to previous calculations in the literature.Comment: 13 pages. important change: running of soft Lagrangian include
The QCD heavy-quark potential to order v^2: one loop matching conditions
The one-loop QCD heavy quark potential is computed to order v^2 in the color
singlet and octet channels. Several errors in the previous literature are
corrected. To be consistent with the velocity power counting, the full
dependence on |p' + p|/|p' - p| is kept. The matching conditions for the NRQCD
one-loop potential are computed by comparing the QCD calculation with that in
the effective theory. The graphs in the effective theory are also compared to
terms from the hard, soft, potential, and ultrasoft regimes in the threshold
expansion. The issue of off-shell versus on-shell matching and gauge dependence
is discussed in detail for the 1/(m k) term in the potential. Matching on-shell
gives a 1/(m k) potential that is gauge independent and does not vanish for
QED.Comment: 28 pages, References added and minor changes to section III, results
unchange
Is symmetry identity?
Wigner found unreasonable the "effectiveness of mathematics in the natural
sciences". But if the mathematics we use to describe nature is simply a coded
expression of our experience then its effectiveness is quite reasonable. Its
effectiveness is built into its design. We consider group theory, the logic of
symmetry. We examine the premise that symmetry is identity; that group theory
encodes our experience of identification. To decide whether group theory
describes the world in such an elemental way we catalogue the detailed
correspondence between elements of the physical world and elements of the
formalism. Providing an unequivocal match between concept and mathematical
statement completes the case. It makes effectiveness appear reasonable. The
case that symmetry is identity is a strong one but it is not complete. The
further validation required suggests that unexpected entities might be
describable by the irreducible representations of group theory
A Critique Of The Disturbance Theory Of Indeterminacy In Quantum Mechanics
Heisenberg's gendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained quasiclassically in terms of a disturbance suffered by the system in interaction with a quantal measurement, or state preparation, agent. There are a number of criticisms of this doctrine in the literature, which are critically examined in this article and found to be ininconclusive, the chief error being the conflation of this disturbance with the projection postulate. We present a critique of the disturbance theory based on the fact that the required disturbance will in general depend on the interaction time of the system and state-preparer. This point is exploited in the construction of a spin-interaction model which acts as a counterexample to the disturbance doctrine, while remaining faithful to the spirit of Heisenberg's gedanken experiments. Several consequences of this result are discussed. © 1981 Plenum Publishing Corporation.111-212
The Characterisation of Structure: Definition versus Axiomatisation
Abstract. We argue that neither the set-theoretical nor the category-theoretical conceptions of structure serve the needs of structural realism, in that they cannot clarify what it means to say that being B is or has structure S, which claim is central to structural realism. Such a clarification is warranted by any viable ac-count of reference, which almost any variety of realism needs. There is however a view that can adopt both set-theoretical and category-theoretical conceptions of structure; this is the view that adopts Bas van Fraassenâs extension of Nelson Good-manâs concept of representation-as from art to science. Yet the ensuing fountain of perspectives is a move away from realism, structural realism included. We then suggest that a new theory of structure is needed, one that takes the word âstruc-ture â to express a primitive fundamental concept; the concept of structure should be axiomatised rather than defined in terms of other concepts. We sketch how such a theory can clarify what it means to say that being B is or has structure S in