Detecting scaling in phase transitions on the truncated Heisenberg algebra

Born-Infeld Electrodynamics and Euler-Heisenberg-like Model: outstanding examples of the lack of commutativity among quantized truncated actions and truncated quantized actions

We calculate the lowest-order corrections to the static potential for both the generalized Born-Infeld Electrodynamics and an Euler-Heisenberg-like model, in the presence of a constant external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a long-range correction ($ {\raise0.7ex\hbox{$1$} \mathord{\left/ {\vphantom {1 {r^5}}}\right.\kern-\nulldelimiterspace} \lower0.7ex\hbox{${r^5}$}}$-type) to the Coulomb potential for the generalized Born-Infeld Electrodynamics. Interestingly enough, in …

One-loop structure of the U(1) gauge model on the truncated Heisenberg space

We calculate divergent one-loop corrections to the propagators of the U(1) gauge theory on the truncated Heisenberg space, which is one of the extensions of the Grosse-Wulkenhaar model. The model is purely geometric, based on the Yang-Mills action; the corresponding gauge-fixed theory is BRST invariant. We quantize perturbatively and, along with the usual wave-function and mass renormalizations, we find divergent nonlocal terms of the $\Box^{-1}$ and $\Box^{-2}$ type. We discuss the meaning of these terms and possible improvements of the model.

On the Heisenberg limit for detecting vacuum birefringence

Quantum electrodynamics predicts the vacuum to behave as a non-linear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg lim…

A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality

For a Hopf algebra B, we endow the Heisenberg double H(B^*) with the structure of a module algebra over the Drinfeld double D(B). Based on this property, we propose that H(B^*) is to be the counterpart of the algebra of fields on the quantum-group side of the Kazhdan--Lusztig duality between logarithmic conformal field theories and quantum groups. As an example, we work out the case where B is the Taft Hopf algebra related to the U_qsl(2) quantum group that is Kazhdan--Lusztig-dual to (p,1) logarithmic conformal models. The corresponding pair (D(B),H(B^*)) is "truncated" to (U_qsl(2),H_qsl(2))…

Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

We construct and analyze the phase diagram of a self-interacting matrix field in two dimensions coupled to the curvature of the non-commutative truncated Heisenberg space. In the infinite size limit, the model reduces to the renormalizable Grosse-Wulkenhaar's. The curvature term proves crucial for the diagram's structure: when turned off, the triple point collapses into the origin as matrices grow larger; when turned on, the triple point recedes from the origin proportionally to the coupling strength and the matrix size. The coupling attenuation that turns the Grosse-Wulkenhaar model into a re…

非交换矩阵模型中三重点的精确定位

Pinpointing Triple Point of Noncommutative Matrix Model with Curvature

该研究通过引入曲率项，改变了非交换矩阵模型的相结构，使其趋向可重整化行为，并发现了新的多切相。