A generating function for fatgraphs
A note concerning the "Feynman integrability" of sets of trajectories
A polynomial invariant of rational homology 3-spheres.
A quantum field theoretical representation of Euler-Zagier sums.
Alternative method for determining the Feynman propagator of a non-relativistic quantum mechanical problem.
Considerations on some algebraic properties of Feynman integrals.
Covariantization of quantized calculi over quantum groups
We introduce a method for construction of a covariant differential calculus over a Hopf algebra from a quantized calculus , , where is a candidate for a Dirac operator for . We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra . We apply this method to the Dirac operator for the quantum given by S. Majid. We find that the differential calculus obtained by our method is the...
Existence of an instanton singularity in . Euclidean field theory
Feynman et les mathématiques
Feynman path integral as spectral decomposition
Generic Feynman amplitudes
Indefinite quadratic functionals of gaussian processes and least-action paths
Introduction aux méthodes euclidiennes en théorie quantique des champs
Lower bounds to Feynman integrals and class
Non-commutative matrix integrals and representation varieties of surface groups in a finite group
A new formula is established for the asymptotic expansion of a matrix integral with values in a finite-dimensional von Neumann algebra in terms of graphs on surfaces which are orientable or non-orientable.
Non-differentiability of Feynman paths
A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof...
On the energy and spectral properties of the he matrix of hexagonal systems
The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles...
Oscillatory Integrals and the Method of Stationary Phase in Infinitely Many Dimensions, with Applications to the Classical Limit of Quantum Mechanics. I.
Remarks on integration over Lie algebras
Shoikhet's conjecture and Duflo isomorphism on (co)invariants.