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Motivated by quantum field theory (QFT) considerations, we present new representations of the Euler-Beta function and tree-level string theory amplitudes using a new two-channel, local, crossing symmetric dispersion relation. Unlike…
A scalar field can be inserted in Maxwell and/or Einstein theory to effect symmetry breaking. Consequences of such a modification are discussed. Possible dynamics for the scalar field are presented.
We use the differential algebra of polytopes to explain the known remarkable relation of the combinatorics of the associahedra and permutohedra with the universal compositional and multiplicative inversion formulas for the formal power…
A detailed comparative qualitative analysis and numerical simulation of evolution of the cosmological models based on classical and phantom scalar fields with self-action was performed. The phase portraits of the dynamic systems of…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We compute tree-level $n$-point scattering amplitudes in scalar field theories in terms of geometric invariants on a fibre bundle. All 0- and 2-derivative interactions are incorporated into a metric on this bundle. The on-shell amplitudes…
It is well known that there should be a total cancellation of the IR divergences in unitary interacting field theories, such as QED and gravity. The cancellation should be at all orders between loop and tree level contributions to…
We report on a comprehensive analysis of the renormalization of noncommutative \phi^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincar\'e invariant. Our main results are that these…
We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to…
D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical…
The tree amplitudes in scalar field theories are presented at all $n$. The momentum routing of propagators is given at $n$-point in terms of a specified set of numbers, and the mass expansion of the massive theories is generated. A group…
Loss of unitarity in an effective field theory is often cured by the appearance of dynamical resonances, revealing the presence of new degrees of freedom. These resonances may manifest themselves when suitable unitarization techniques are…
We study planar noncommutative theories such that the spatial coordinates ${\hat x}_1$, ${\hat x}_2$ verify a commutation relation of the form: $[{\hat x}_1, {\hat x}_2] = i \theta ({\hat x}_1,{\hat x}_2)$. Starting from the operatorial…
Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial…
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical…
Nonrenormalizable scalar fields, such as \varphi^4_n, n\ge5, require infinitely many distinct counter terms when perturbed about the free theory, and lead to free theories when defined as the continuum limit of a lattice regularized theory…
We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories.…
The spectral theory of the Laplace differential operator for biregular quantum graphs is developed. Trees are studied in detail. Generating functions for closed non backtracking walks appear when resolvents for trees are related to…
Here we perform the Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized…
We perform the analysis of the trispectrum of curvature perturbations generated by the interactions characterizing a general theory of single-field inflation obtained by effective field theory methods. We find that curvature-generated…