Related papers: Loop Vertex Expansion for Higher Order Interaction…
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength,…
We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where…
The generic structure of 1-, 2- and 3-point functions of fields residing in indecomposable representations of arbitrary rank are given. These in turn determine the structure of the operator product expansion in logarithmic conformal field…
We construct an off-shell extension of cubic interaction vertices between massless bosonic Higher Spin fields on a flat background which can be obtained from perturbative bosonic string theory. We demonstrate how to construct higher quartic…
Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE,…
We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Relying on Hepp's method and a detailed analysis of the associated classical and quantum field…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
An expression of partial wave expansion of three-baryon interactions in chiral effective field theory is presented. The derivation follows the method by Hebeler et al. [Phys. Rev. C{\bf 91}, 044001 (2015)], but the final expression is more…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
Using the light-cone formulation of relativistic dynamics, we develop various methods for constructing cubic interaction vertices and apply these methods to the study of higher spin fields propagating in flat space of dimension greater than…
Graph rules for the linked cluster expansion of the Legendre effective action $\Gamma[\phi]$ are derived and proven in $D\geq 2$ Euclidean dimensions. A key aspect is the weight assigned to articulation vertices which is itself shown to be…
This work presents author's explicit methods of constructing abelian extensions of complete discrete valuation fields. His approach to explicit equations of a cyclic extension of degree p^n which contains a given cyclic extension of degree…
We consider the large order behavior of the perturbative expansion of the scalar $\varphi^4$ field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order…
Effective field theories include contact-range interactions (or counterterms) for two reasons: representing the unknown short-range physics in a model independent manner and ensuring the cutoff independence of observables. Both are…
Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.
Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then, by considering the same class of infinite interacting…
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…
We use generating functionals to derive a dynamic mean-field description for generalised Lotka-Volterra systems with higher-order quenched random interactions. We use the resulting single effective species process to determine the stability…
Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…