Conveners
W3-2 Mathematical and Theoretical Physics (DTP) / Physique mathématique et physique théorique (DPT)
- Thomas Creutzig (University of Alberta)
We numerically analyze the spectrum of the Laplacian on the moduli space of a genus zero Riemann surface with four punctures via a perturbative expansion of the path integral of Liouville theory. Our results furnish evidence that the eigenvalues obey the statistics of a random matrix in the Gaussian Orthogonal Ensemble. We comment on possible implications for the quantum geometry of Riemann...
We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general dimension. These spaces are paired via an inner product called the intersection number -- an invariant which can be computed algebraically. In this language, reduction of an integrand modulo integration-by-part identities is simply its...
We describe the offset logarithm function and illustrate its applications to physics. The offset log can be considered an extension of the logarithm function, and it can also be considered as a generalization of the Lambert W function.
The offset log function shows up in a variety of physical and biological models, such as the mean field model (Weiss model) of ferromagnetism, and models...
Approximation of the ground state wave function and energy of a quantum system is often achieved using perturbation theory or the variational method. The former approach suffers from the requirement that the Hamiltonian perturbation be small enough for the series to converge while the variational method is only as good as the choice of functions used in the expansion, providing only an...
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to relate classical polymer self-consistent field theory to quantum density functional theory. This allows the theorems of density functional theory, which connect single particle density descriptions of quantum systems to wave function...
THESIS: The ontology of spacetime should not be modelled as a single universally-shared 4D spacetime manifold.
THE CONSENSUS SPACETIME ONTOLOGY: The accepted ontology of classical spacetime is of a 4D differentiable manifold of events. Although different observers may assign different coordinate labels to events, it is conventionally asserted that the underlying reality is that of a...
