Related papers: Lipatov's Effective Action Beyond Tree Level
A strongly interacting Fermi gas, such as that of cold atoms operative near a Feshbach resonance, is difficult to study by perturbative many-body theory to go beyond mean field approximation. Here I develop an effective field theory for the…
We study group actions on multitrees, which are directed graphs in which there is at most one directed path between any two vertices. In our main result we describe a six-term exact sequence in $K$-theory for the reduced crossed product…
We propose a hybrid combination of active inference and behavior trees (BTs) for reactive action planning and execution in dynamic environments, showing how robotic tasks can be formulated as a free-energy minimization problem. The proposed…
The human-like reasoning capabilities exhibited by Large Language Models (LLMs) challenge the traditional neural network theory's understanding of the flexibility of fixed-parameter systems. This paper proposes the "Cognitive Activation"…
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep…
In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with…
This paper provides a derivation of Zipf-Pareto laws directly from the principle of least effort. A probabilistic functional of efficiency is introduced as the consequence of an extension of the nonadditivity of the efficiency of…
The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in…
We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss…
We consider the Sudakov form factor in effective theories and we show that one can derive correctly the double logarithms of the original, high-energy, theory. We show that in effective theories it is possible to separate explicitely soft…
High orders in perturbation theory can be calculated by the Lipatov method. For most field theories, the Lipatov asymptotics has the functional form c a^N \Gamma(N+b) (N is the order of perturbation theory); relative corrections to this…
I review the use of the 2PI effective action in nonequilibrium quantum field theory. The approach enables one to find approximation schemes which circumvent long-standing problems of non-thermal or secular (unbounded) late-time evolutions…
A non-subtractive recipe of Casimir energy renormalization efficient in the presence of logarithmically divergent terms is proposed. It is demonstrated that it can be applied even in such cases, when energy levels can be obtained only…
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…
We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact…
In this note we derive Dyson-Schwinger hierarchy of the equations for the correlators of reggeized gluon fields in the framework of Lipatov's high energy QCD effective action formalism, \cite{LipatovEff,Our1,Our2,Our3,Our4}. The explicit…
We give two kinds of approximation of Lyapunov exponents of rational functions of degree more than one on the projective line over more general fields than that of complex numbers.
This paper introduces effectful toposes as an extension of the effective topos and investigates their structure relative to Lawvere-Tierney topologies. First, we formulate effectful toposes by lifting the evidenced frame, which is a…
We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical…
We focus on modeling the relationship between an input feature vector and the predicted outcome of a trained decision tree using mixed-integer optimization. This can be used in many practical applications where a decision tree or tree…