相关论文: Non Local Theories: New Rules for Old Diagrams
Recent developments in quantum chemistry, perturbative quantum field theory, statistical physics or stochastic differential equations require the introduction of new families of Feynman-type diagrams. These new families arise in various…
We discuss the perturbative approach a` la Dyson to a quantum field theory with nonlocal self-interaction :phi*...*phi:, according to Doplicher, Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction of non locally…
In the models defined on the inhomogeneous background the propagators depend on the two space - time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations…
The Wick rotation provides the standard technique of computing Feynman diagrams by means of Euclidean propagators. Let us suppose that quantum fields in an interaction zone are really Euclidean. In contrast with the well-known Euclidean…
As argued previously, amplitudes of quantum field theories on noncommutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann--Low formula with time-ordering applied…
We show that a class of matrix theories can be understood as an extension of quantum field theory which has non-local interactions. This reformulation is based on the Wigner-Weyl transformation, and the interactions take the form of Moyal…
In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to…
In the past decades, time ordered perturbation theory was very successful in describing relativistic scattering processes. It was developed for local quantum field theories. However, there are field theories which are governed by non-local…
Twisted quantum field theories on the Groenewold-Moyal plane are known to be non-local. Despite this non-locality, it is possible to define a generalized notion of causality. We show that interacting quantum field theories that involve only…
Partition- and moment functions for a general (not necessarily Gaussian) functional measure that is perturbed by a Gibbs factor are calculated using generalized Feynman graphs. From the graphical calculus, a new notion of Wick ordering…
On a large class of asymptotically flat spacetimes which includes radiative perturbations of Minkowski space, we define a distinguished global Feynman propagator for massive Klein-Gordon fields by means of the microlocal approach to…
In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler--Lagrange equations,…
A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus $g$ 2-surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes…
It is shown that the usual expression for a Feynman diagram in terms of the Feynman propagator $\Delta_F(x-y)$ can be replaced by an equivalent expression involving the positive-energy on-shell propagator $\Delta^+(x-y)$, supplemented by…
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the…
A representation of the perturbation series of a general functional measure is given in terms of generalized Feynman graphs and -rules. The graphical calculus is applied to certain functional measures of L\'evy type. A graphical notion of…
I work on a set of Feynman rules that were derived in order to incorporate the constraint of Gauss's law in the perturbation expansion of gauge field theories and calculate the interaction energy of two static sources. The constraint is…
This paper derives the Feynman rules for the diagrammatic perturbation expansion of the effective action around an arbitrary solvable problem. The perturbation expansion around a Gaussian theory is well known and composed of one-line…
The paper considers quantum electrodynamics (QED) and weak interaction of elementary particles in the lower orders of the perturbation theory using nonlocal Hamiltonian in the Foldy-Wouthuysen (FW) representation. Feynman rules in the FW…
Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…