相关论文: Feynman Diagrams in Algebraic Combinatorics
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve…
We report on recent results on the Quantum Field Theory of mixed particles. The quantization procedure is discussed in detail, both for fermions and for bosons and the unitary inequivalence of the flavor and mass representations is proved.…
A very general calculational strategy is applied to the evaluation of the divergent physical amplitudes which are typical of perturbative calculations. With this approach in the final results all the intrinsic arbitrariness of the…
We present a new group field theory model, generalising the Boulatov model, which incorporates both 3-dimensional gravity and matter coupled to gravity. We show that the Feynman diagram amplitudes of this model are given by Riemannian…
In this paper we will demonstrate the use of Feynman Diagrams for one dimensional scattering in quantum mechanics. We will evaluate the S-Matrix explicitly for the Dirac delta and finite wall potentials by summing the full series of Feynman…
We classify combinatorial Dyson-Schwinger equations giving a Hopf subalgebra of the Hopf algebra of Feynman graphs of the considered Quantum Field Theory. We first treat single equations with an arbitrary number (eventually infinite) of…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…
We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an emphasis on further directions of research.
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
We analyze numerically a two-dimensional $\lambda\phi^4$ theory showing that in the limit of a strong coupling $\lambda\to\infty$ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in…
The quantum field theory in the presence of classical background electromagnetic fields is reviewed. We give a pedagogical introduction to the Feynman-Furry method of describing non-perturbative interactions with very strong electromagnetic…
We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like the Ramond algebra). In particular, we…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…
Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…
We provide a novel representation of the total n-th derivative of the multivariate composite function $f \circ g$, i.e. a generalized Fa\`a di Bruno's formula. To this end, we make use of properties of the Kronecker product and the n-th…
This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic structure of the asymptotics of formal power…