Light Quantization Module (LQM): Theory & Applications

• LQM is a framework that explicitly quantizes illumination as a core physical attribute in both quantum field theory and image enhancement.
• It enables systematic light-front quantization and adaptive renormalization in QED, yielding electron magnetic moment calculations with ~0.06% precision.
• In computational vision, LQM disentangles global lighting using Gram matrices and contrastive losses, improving low-light image quality and texture recovery.

The Light Quantization Module (LQM) refers to a class of modules appearing in various research domains—most notably in nonperturbative quantum field theory (QFT) and low-light image enhancement—where the quantization, extraction, or explicit structuring of “light” or illumination-related attributes is essential. LQMs are characterized by their explicit treatment of illumination as either a quantum-field attribute (in the context of light-front quantization) or as a global image style (in computer vision), leveraging dedicated mathematical tools and loss functions to induce invariance or disentanglement between illumination conditions and underlying content.

1. Theoretical Underpinnings in Light-Front Quantization

In Hamiltonian-based nonperturbative QFT, the LQM concept is exemplified by the Basis Light-Front Quantization (BLFQ) framework. Here, quantization is performed on the light-front slice of spacetime (with coordinates $x^+ = x^0 + x^3$ and $x^- = x^0 - x^3$), resulting in a reformulation of canonical commutation relations and Fock-state bases (Zhao et al., 2014, Zhao, 2014, Mannheim, 2019). BLFQ uses basis truncations (via $N_{\text{max}}$ and $K$ parameters) that regularize both ultraviolet and infrared divergences and yield a discrete Hilbert space suitable for high-dimensional Hamiltonian diagonalization. LQM in this context denotes the systematic construction of light-front Hamiltonians, operator expansions in suitable bases, and related nonperturbative computation of physical observables.

The equivalence between light-front and instant-time quantization—despite seemingly distinct canonical structures and projections—was established by tracking unequal-time commutators and spectral representations. This ensures that the LQM, as implemented in light-front settings, is mathematically and physically consistent with the traditional instant-form approach (Mannheim, 2019).

2. LQM in Quantum Electrodynamics: Practical Construction

For problems such as the calculation of the electron anomalous magnetic moment $a_e$, the LQM framework employs a sector-truncated Fock expansion (e.g., $|e\rangle$ and $|e\gamma\rangle$ in QED) and constructs the light-front QED Hamiltonian in the form:

$$P^- = \int d^2x_\perp dx^- \left[ \frac{1}{2} \bar{\psi} \left( \gamma^+ \frac{m_e^2 + (i \partial_\perp)^2}{i \partial^+} \right) \psi + \frac{1}{2} A^j (i \partial_\perp)^2 A^j + e j^\mu A_\mu \right]$$

where basis states are labeled by quantum numbers related to harmonic oscillator and plane wave functions for transverse and longitudinal directions, respectively (Zhao et al., 2014). Observables are extracted from diagonalization results, with systematic renormalization (through iterative parameter adjustment and wavefunction rescaling) ensuring physical mass and the restoration of broken symmetries, such as the Ward identity.

Notably, the calculation of $a_e$ requires compensating for Fock-space truncation effects. Here, LQM techniques dictate dividing the Pauli form factor $F_2(0)$ by the wavefunction renormalization:

$a_e = F_2(0) / Z_2$

where $Z_2 = \sum_{|e\rangle} |\text{amplitude}|^2$ is the probability of the bare electron sector. Such approaches yield agreement with the Schwinger result at $0.06\%$ precision (Zhao et al., 2014).

3. Structured Renormalization and Basis Adaptation

In BLFQ and related LQM methodologies, further extensions involve basis-state-dependent renormalization, especially in multi-particle systems like positronium (Zhao, 2014). Here, basis-dependent parameters $\Delta m$ and $Z_2$ are extracted via embedded single electron (ESE) systems, ensuring that self-energy corrections reflect both physical and computational constraints inherent to the basis truncation. Observables are consistently evaluated as differences between positive-norm and negative-norm component contributions in each rescaled amplitude, ensuring consistency and correct normalization even under sector truncation.

These systematic basis-adaptive procedures are crucial for extending the reach of LQM techniques toward non-Abelian gauge theories and multi-body QFT contexts, where basis construction and renormalization protocols must be explicitly maintained sector-by-sector.

4. LQM in Computational Vision: Explicit Illumination Structuring

In computer vision, the LQM concept is instantiated in frameworks such as LightQANet, which addresses the problem of low-light image enhancement (Wu et al., 16 Oct 2025). Here, the LQM is a dedicated neural network sub-module that explicitly quantifies and structures illumination information (the “light factor”) from intermediate feature maps. It models illumination as a global style, represented by Gram matrices $G = a^\top a$, where $a$ is the channel-wise feature activation matrix. This approach draws upon successful style-transfer representations and enables the network to disentangle global illumination from image content.

The LQM is trained using a supervised contrastive loss to map images with similar lighting into proximate regions of the light factor space while maximizing separation for images from different lighting conditions. The contrastive loss for light factors $f^{(a,l)}$ and $f^{(b,l)}$ at layer $l$ is:

$$\mathcal{L}_{\mathrm{lqm}} = \sum_{(a, b) \in \mathcal{P}} \left\{ (1 - \mathbb{1}(a, b)) [m - d(f^{(a,l)}, f^{(b,l)})]_+^2 + \mathbb{1}(a, b) [d(f^{(a,l)}, f^{(b,l)}) - m]_+^2 \right\}$$

where $d(\cdot, \cdot)$ is a distance (e.g., cosine similarity) and $m$ is a margin. Subsequently, an auxiliary light consistency loss enforces that the encoder features map low-light and normal-light images to similar light factors, yielding robust, light-invariant representations.

5. Numerical and Empirical Outcomes

LQM-based approaches in BLFQ have achieved benchmark precision in QED observables, notably extracting $a_e$ with deviations below $0.06\%$ from perturbative theory in QED (Zhao et al., 2014). The modular and computationally efficient design—leveraging parallel diagonalization and extrapolation methods—renders LQM scalable and adaptable for larger Hamiltonians and higher-dimensional basis spaces.

In vision tasks, the LQM within LightQANet has empirically demonstrated improved restoration quality under low-light conditions, as measured by PSNR/SSIM and activation distribution analysis. Images processed with LQM-enhanced models exhibit more consistent feature representations across lighting conditions, improved texture recovery, and reduced artifacts compared to models lacking explicit illumination structuring (Wu et al., 16 Oct 2025).

6. Methodological Generalization and Impact

The LQM paradigm, as realized across quantum field theory and computational imaging, systematically incorporates illumination quantization and structuring at the level of fundamental operator bases or feature spaces. In QFT, this involves explicit basis construction, operator expansion, sector truncation, and renormalization—yielding a nonperturbative, regularized framework for bound-state computations. In computer vision, it uses matrix-based characterization of light, contrastive learning, and consistency supervision to capture illumination as a latent attribute.

A plausible implication is that these methodology-agnostic principles—explicit quantization of “light” or illumination, structured separation from content, and regularization—are transferrable to other domains where disentangling or precisely structuring global attributes from detailed representations is needed.

7. Summary Table: LQM Across Domains

Domain	LQM Principle	Main Techniques
Quantum Field Theory (BLFQ)	Light-front basis quantization, truncation	Harmonic oscillator + plane wave basis, sector-dependent renormalization, rescaling for Ward identity restoration
Low-Light Image Enhancement (LightQANet)	Explicit light factor extraction and structuring	Gram matrix computation, supervised contrastive and consistency losses

The LQM framework thus encompasses a set of mathematically principled methodologies for explicit quantization and structuring of light-related attributes, leading to improved physical observables in field theory and enhanced robustness in low-light computational vision systems.