1.1. About these lecture notes. For centuries physics was a potent source providing mathematics with interesting ideas and problems. In the last decades something new started to happen: physicists started to provide mathematicians also with technical tools, methods, and solutions. This process seem to be especially strong in geometry and low-dimensional topology. It is enough to mention the mir...

During the 1962–63 academic year, Richard Feynman taught a course at Caltech on gravitation. Taking an untraditional approach to the subject, Feynman aimed the course at advanced graduate students and postdoctoral fellows who were familiar with the methods of relativistic quantum field theory—in particular, with Feynman-diagram perturbation theory in quantum electrodynamics. Two of the postdocs...

Starting from the Mellin–Barnes integral representation of a Feynman depending on set kinematic variables zi, we derive system partial differential equations w.r.t. new xj, which parameterize differentiable constraints zi=yi(xj). In our algorithm, powers propagators can be considered as arbitrary parameters. Our algorithm also used for reduction multiple hypergeometric sums to lower dimension, ...

We examine contributions to the muon dipole moment $g-2$ from a 3-form field $\Omega$, which naturally arises many fundamental theories, such as string theory and hyperunified theory. In particular, by calculating one-loop Feynman diagram, we have obtained leading-order $\Omega$-induced contribution $g-2$, is found be finite. Then investigate theoretical constraints perturbativity unitarity. Es...

Nonlocal gluon condensates are vacuum expectations of the product field strength tensors. Short-distance expansions two-, three-, and four-gluon presented up to dimension-eight local operators. We propose a method for calculating Wilson coefficients based on Feynman diagram technique in background approach. The is demonstrated using glueball current correlators as examples. Methodological aspec...

We study the stationary descendant Gromov–Witten theory of toric surfaces by combining and extending a range techniques – tropical curves, floor diagrams Fock spaces. A correspondence theorem is established between curves invariants on using maximal degenerations. An intermediate degeneration then shown to give rise diagrams, giving geometric interpretation this well-known bookkeeping tool in g...

The sign cancellation between scattering amplitudes makes fermions different from bosons. We systematically investigate Feynman diagrams' fermionic structure in a representative many-fermion system---a uniform Fermi gas with Yukawa interaction. analyze the role of crossing symmetry and global gauge cancellation. arguments are then used to identify sign-canceled groups diagrams. Sign-structure a...

It is shown that the processes of neutrino oscillations in a magnetic field can be consistently described framework new quantum field-theoretical approach without use flavor states. based on Feynman diagram technique with modified distance-dependent propagator, which takes into account geometry oscillation experiments. Processes field, where neutrinos are detected through weak charged- and neut...

The Feynman checkerboard problem is an interesting path integral approach to the Dirac equation in ‘1+1’ dimensions. I compare two approaches reported in the literature and show how they may be reconciled. Some physical insights may be gleaned from this approach.