Category: HEISINGBERG

Localization in quantum field theory (a review)

We review the localization issue in quantum field theory and detail the nonrelativistic limit. Three distinct localization schemes are examined: the Newton–Wigner, the algebraic quantum field theory, and the modal scheme. Among these, the algebraic quantum field theory provides a fundamental concept of localization rooted in its axiomatic formulation. In contrast, the Newton–Wigner scheme draws inspiration from the Born interpretation, applying mainly to the nonrelativistic regime. The modal scheme, relying on the representation of single particles as positive frequency modes of the Klein–Gordon equation, is found to be incompatible with the algebraic quantum field theory localization.
This review delves into the distinctive features of each scheme, offering a comparative analysis. A specific focus is placed on independence between state preparations and observable measurements in spacelike-separated regions. Notably, localization in algebraic quantum field theory violates this independence due to the Reeh–Schlieder theorem. Drawing parallels with the quantum teleportation protocol, it is argued that causality remains unviolated. Additionally, we consider the nonrelativistic limit of quantum field theory, revealing the emergence of the Born scheme as the fundamental concept of localization. Consequently,
the nonlocality associated with the Reeh–Schlieder theorem is shown to be suppressed under nonrelativistic conditions.

https://doi.org/10.1016/j.revip.2024.100095

(see also Localization in Quantum Field Theory for Inertial and Accelerated Observers)

Efficient Computation Using Spatial-Photonic Ising Machines: Utilizing Low-Rank and Circulant Matrix Constraints

https://arxiv.org/abs/2406.01400

We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices. By developing and assessing advanced decomposition techniques, we expand the range of problems SPIMs can solve, overcoming the limitations of traditional Mattis-type matrices. Our approach accommodates a diverse array of coupling matrices, including those with inherently low ranks, applicable to complex NP-complete problems. We explore the practical benefits of low-rank approximation in optimization tasks, particularly in financial optimization, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimize the performance of these systems within these constraints.