Related papers: Holonomy observables in Ponzano-Regge type state s…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
We introduce a notion of s-holomorphicity suitable for certain quantum spin systems in one dimension, and define two observables in the critical transverse-field Ising model which have this property. The observables are defined using…
We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum over topologically distinct gauge…
We study the compactly supported rational cohomology of configuration spaces of points on wedges of spheres, equipped with natural actions of the symmetric group and the group $Out(F_g)$ of outer automorphisms of the free group. These…
We study how the problem of observables is fully resolved for background independent theories defined on finite graphs. We argue the correct analogue of coordinate independence is the invariance under changes of graph labels, a kind of…
We show in several important cases that the $A$-hypergeometric system attached to a Feynman diagram in Lee--Pomeransky form, obtained by viewing the momenta and the nonzero masses as indeterminates, has a normal underlying semigroup. This…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract…
We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have…
Using a one-to-one correspondence between observables and their spectral resolutions, we introduce the sum of any two bounded observables of a $\sigma$-MV-effect algebra. This sum is commutative, associative and with neutral element. Under…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized…
We provide a combinatorial model for spin surfaces. Given a triangulation of an oriented surface, a spin structure is encoded by assigning to each triangle a preferred edge, and to each edge an orientation and a sign, subject to certain…
In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used for 2d quantum gravity. In particular…
It is shown that the non-relativistic `Dirac' equation of L\'evy-Leblond, we used recently to describe a spin $1/2$ field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from $3+1$…
Three-dimensional gravity is a topological field theory, which can be quantized as the Ponzano-Regge state-sum model built from the $\{3nj\}$-symbols of the recoupling of the $\SU(2)$ representations, in which spins are interpreted as…
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…
This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from…
Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic spin-fermion model in a one-dimensional lattice,…
Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…