Quantum Field Theory and System Theory

Meinard Kuhlmann, Manfred Stöckler

Kantaro Ohmori, Shutaro Shimamura

There has been proposed two continuum descriptions of fracton systems: foliated quantum field theories (FQFTs) and exotic quantum field theories. Certain fracton systems are believed to admit descriptions by both, and hence a duality is expected between such a class of FQFTs and exotic QFTs. In this paper we study this duality in detail for concrete examples in 2+1 2 + 1 and 3+1 3 + 1 dimensions. In the examples, both sides of the continuum theories are of BF B F -type, and we find the explicit correspondences of gauge-invariant operators, gauge fields, parameters, and allowed singularities and discontinuities. This deepens the understanding of dualities in fractonic quantum field theories.

Armin Uhlmann

Jincheng Zhang

The current state of quantum field theory (QFT) often relies on static models, limiting its ability to accurately describe complex phenomena. This paper introduces Adaptive Quantum Field Theory (AQTF), a novel framework that dynamically evolves quantum fields in response to external inputs. We propose a mechanism centered on utilizing quantum field theory to enable fields to evolve in a self-organizing manner, fostering emergent behavior and allowing for dynamic system formation. This research addresses limitations of existing QFT models by introducing a core principle of self-generated field evolution. The framework incorporates a dynamic adjustment algorithm to guide field evolution, resulting in a system capable of adapting to changing environmental conditions. The core claim is that AQTF provides a pathway towards creating truly adaptive and self-organizing quantum systems, exceeding the capabilities of traditional static QFT models. The theoretical foundation is built upon a modified approach to the Schrödinger equation, incorporating feedback loops and adaptive adjustments to maintain field coherence and stability. This work explores the potential for AQTF to yield novel quantum phenomena and provide a foundation for advanced computational modeling.

H.-J. Unger

Rajendran, Praveen Kizhakkeveedu

This work presents a rigorous derivation of a relativistic quantum field theory (QFT) as the long-wavelength, low-energy limit of a microscopic quantum many-body system defined by the Advaita Chakra Theory (ACT). The ACT model consists of a lattice of quantum rotors with compact angular variables (“chakras”) interacting via local, translation-invariant couplings. In the fully locked phase, the Goldstone sector of ACT gives rise to a massless scalar field theory on an emergent Lorentzian spacetime. Using tools from lattice field theory, Lieb–Robinson bounds, and constructive QFT, we establish convergence of correlation functions, microcausality, and Lorentz invariance in the scaling limit. The resulting field satisfies the Wightman axioms and supports a local effective field theory at low energies. This result provides a concrete example of how relativistic QFT can emerge from a discrete, nonrelativistic quantum system via continuum scaling and coarse-graining.