5,708 research outputs found
Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators
The symmetric interaction combinators are an equally expressive variant of
Lafont's interaction combinators. They are a graph-rewriting model of
deterministic computation. We define two notions of observational equivalence
for them, analogous to normal form and head normal form equivalence in the
lambda-calculus. Then, we prove a full abstraction result for each of the two
equivalences. This is obtained by interpreting nets as certain subsets of the
Cantor space, called edifices, which play the same role as Boehm trees in the
theory of the lambda-calculus
The relational model is injective for Multiplicative Exponential Linear Logic
We prove a completeness result for Multiplicative Exponential Linear Logic
(MELL): we show that the relational model is injective for MELL proof-nets,
i.e. the equality between MELL proof-nets in the relational model is exactly
axiomatized by cut-elimination.Comment: 33 page
The relational model is injective for Multiplicative Exponential Linear Logic (without weakenings)
We show that for Multiplicative Exponential Linear Logic (without weakenings)
the syntactical equivalence relation on proofs induced by cut-elimination
coincides with the semantic equivalence relation on proofs induced by the
multiset based relational model: one says that the interpretation in the model
(or the semantics) is injective. We actually prove a stronger result: two
cut-free proofs of the full multiplicative and exponential fragment of linear
logic whose interpretations coincide in the multiset based relational model are
the same "up to the connections between the doors of exponential boxes".Comment: 36 page
Motivations and Physical Aims of Algebraic QFT
We present illustrations which show the usefulness of algebraic QFT. In
particular in low-dimensional QFT, when Lagrangian quantization does not exist
or is useless (e.g. in chiral conformal theories), the algebraic method is
beginning to reveal its strength.Comment: 40 pages of LateX, additional remarks resulting from conversations
and mail contents, removal of typographical error
Taylor expansion in linear logic is invertible
Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded
into a differential net, which is its Taylor expansion. We prove that two
different MELL proof-nets have two different Taylor expansions. As a corollary,
we prove a completeness result for MELL: We show that the relational model is
injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the
relational model is exactly axiomatized by cut-elimination
An Explicit Framework for Interaction Nets
Interaction nets are a graphical formalism inspired by Linear Logic
proof-nets often used for studying higher order rewriting e.g. \Beta-reduction.
Traditional presentations of interaction nets are based on graph theory and
rely on elementary properties of graph theory. We give here a more explicit
presentation based on notions borrowed from Girard's Geometry of Interaction:
interaction nets are presented as partial permutations and a composition of
nets, the gluing, is derived from the execution formula. We then define
contexts and reduction as the context closure of rules. We prove strong
confluence of the reduction within our framework and show how interaction nets
can be viewed as the quotient of some generalized proof-nets
Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix
It has been known that the Wigner representation theory for positive energy
orbits permits a useful localization concept in terms of certain lattices of
real subspaces of the complex Hilbert -space. This ''modular localization'' is
not only useful in order to construct interaction-free nets of local algebras
without using non-unique ''free field coordinates'', but also permits the study
of properties of localization and braid-group statistics in low-dimensional
QFT. It also sheds some light on the string-like localization properties of the
1939 Wigner's ''continuous spin'' representations.We formulate a constructive
nonperturbative program to introduce interactions into such an approach based
on the Tomita-Takesaki modular theory. The new aspect is the deep relation of
the latter with the scattering operator.Comment: 28 pages of LateX, removal of misprints and extension of the last
section. more misprints correcte
Glueability of Resource Proof-Structures: Inverting the Taylor Expansion
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures
Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
The perturbative treatment of quantum field theory is formulated within the
framework of algebraic quantum field theory. We show that the algebra of
interacting fields is additive, i.e. fully determined by its subalgebras
associated to arbitrary small subregions of Minkowski space. We also give an
algebraic formulation of the loop expansion by introducing a projective system
of observables ``up to loops'' where is
the Poisson algebra of the classical field theory. Finally we give a local
algebraic formulation for two cases of the quantum action principle and compare
it with the usual formulation in terms of Green's functions.Comment: 29 page
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