144,698 research outputs found
The Structure of First-Order Causality
Game semantics describe the interactive behavior of proofs by interpreting
formulas as games on which proofs induce strategies. Such a semantics is
introduced here for capturing dependencies induced by quantifications in
first-order propositional logic. One of the main difficulties that has to be
faced during the elaboration of this kind of semantics is to characterize
definable strategies, that is strategies which actually behave like a proof.
This is usually done by restricting the model to strategies satisfying subtle
combinatorial conditions, whose preservation under composition is often
difficult to show. Here, we present an original methodology to achieve this
task, which requires to combine advanced tools from game semantics, rewriting
theory and categorical algebra. We introduce a diagrammatic presentation of the
monoidal category of definable strategies of our model, by the means of
generators and relations: those strategies can be generated from a finite set
of atomic strategies and the equality between strategies admits a finite
axiomatization, this equational structure corresponding to a polarized
variation of the notion of bialgebra. This work thus bridges algebra and
denotational semantics in order to reveal the structure of dependencies induced
by first-order quantifiers, and lays the foundations for a mechanized analysis
of causality in programming languages
Wave propagation in axion electrodynamics
In this paper, the axion contribution to the electromagnetic wave propagation
is studied. First we show how the axion electrodynamics model can be embedded
into a premetric formalism of Maxwell electrodynamics. In this formalism, the
axion field is not an arbitrary added Chern-Simon term of the Lagrangian, but
emerges in a natural way as an irreducible part of a general constitutive
tensor.We show that in order to represent the axion contribution to the wave
propagation it is necessary to go beyond the geometric approximation, which is
usually used in the premetric formalism. We derive a covariant dispersion
relation for the axion modified electrodynamics. The wave propagation in this
model is studied for an axion field with timelike, spacelike and null
derivative covectors. The birefringence effect emerges in all these classes as
a signal of Lorentz violation. This effect is however completely different from
the ordinary birefringence appearing in classical optics and in premetric
electrodynamics. The axion field does not simple double the ordinary light cone
structure. In fact, it modifies the global topological structure of light cones
surfaces. In CFJ-electrodynamics, such a modification results in violation of
causality. In addition, the optical metrics in axion electrodynamics are not
pseudo-Riemannian. In fact, for all types of the axion field, they are even
non-Finslerian
The conformal window in QCD and supersymmetric QCD
In both QCD and supersymmetric QCD (SQCD) with N_f flavors there are
conformal windows where the theory is asymptotically free in the ultraviolet
while the infrared physics is governed by a non-trivial fixed-point. In SQCD,
the lower N_f boundary of the conformal window, below which the theory is
confining is well understood thanks to duality. In QCD there is just a
sufficient condition for confinement based on superconvergence. Studying the
Banks-Zaks expansion and analyzing the conditions for the perturbative coupling
to have a causal analyticity structure, it is shown that the infrared
fixed-point in QCD is perturbative in the entire conformal window. This finding
suggests that there can be no analog of duality in QCD. On the other hand in
SQCD the infrared region is found to be strongly coupled in the lower part of
the conformal window, in agreement with duality. Nevertheless, we show that it
is possible to interpolate between the Banks-Zaks expansions in the electric
and magnetic theories, for quantities that can be calculated perturbatively in
both. This interpolation is explicitly demonstrated for the critical exponent
that controls the rate at which a generic physical quantity approaches the
fixed-point.Comment: Journal versio
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