LLMs Can Tackle High Energy Theoretical Physics, yet Gaps Remain: Part I, Quantum Field Theory

Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field theory and string theory. Evaluating this possibility faces an immediate challenge: correctness in these domains is layered, tacit, and fundamentally non-binary. Standard answer-matching metrics fail to capture whether intermediate conceptual steps are properly reconstructed or whether implicit structural constraints are respected. We construct a compact expert-curated dataset of twelve questions spanning core areas of quantum field theory and string theory, and introduce a five-level grading rubric separating statement correctness, key concept awareness, reasoning chain presence, tacit step reconstruction, and enrichment. Evaluating multiple contemporary LLMs, we observe near-ceiling performance on explicit derivations within stable conceptual frames, but systematic degradation when tasks require reconstruction of omitted reasoning steps or reorganization of representations under global consistency constraints. These failures are driven not only by missing intermediate steps, but by an instability in representation selection: models often fail to identify the correct conceptual framing required to resolve implicit tensions. We argue that highly abstract theoretical physics provides a uniquely sensitive lens on the epistemic limits of current evaluation paradigms.

Despite the growing application of large language models (LLMs) to theoretical physics, there has been little academic exploration of how domain-specific physics reasoning ability develops during training. To investigate this, we perform the first academic comparison of reinforcement learning and supervised fine-tuning for LLMs on verifiable problem-solving tasks in theoretical physics. Because the open-source verifiable training data required to develop such capabilities is scarce, we built a robust data generation pipeline that can both create synthetic problems and make existing human-authored problems suitable for model training. Selecting quantum field theory (QFT) as our primary domain, we generated over 2,500 synthetic problems alongside a curated collection of human-adapted problems sourced from arXiv and standard pedagogical resources. We conduct both reinforcement learning (RL) and supervised fine-tuning (SFT) experiments, benchmarking performance gains as well as generalization to other physics domains. Although both methods improve over the base model on every dataset, SFT gains are concentrated on in-distribution synthetic tasks, while RL generalizes better, outperforming SFT on the human-adapted datasets and TPBench. We perform an extensive analysis of model chain-of-thought (CoT) reasoning before and after fine-tuning to understand how reasoning errors evolve during RL and SFT. Finally, we publicly release our data pipeline, verifiable QFT training data, and ~200M tokens of QFT reasoning traces.

Current large-language-model (LLM) physics benchmarks are usually scored by answer accuracy, which cannot distinguish genuine reasoning from recall of familiar problem patterns and reveals little about where a model's reasoning breaks down. We introduce an auditable four-stage diagnostic that evaluates whether an LLM can reason inside an unfamiliar physics framework through induction, formulation, prediction, and review. The diagnostic combines locked pre-registrations, fresh sessions between stages, dual-LLM judging, and a human-audit pathway, and we apply it to three parallel physics worlds: a single-equation counterfactual world ($F=mv$), a historical framework (Aristotelian mechanics), and a four-domain counterfactual world (Decay World). Across Claude Opus 4.7, GPT-5.5, and Gemini 3.1 Pro, the three worlds yield composite PASS rates are 6/15, 6/15, and 0/15 respectively (content $\land$ structural for $F=mv$ and Aristotelian, content axis only for Decay World where the structural axis is out of scope). The most pointed empirical pattern is a qualitative-versus-quantitative asymmetry: in Decay World, models almost never predict the wrong direction of change, but frequently compute the wrong ratio by slipping back to standard-physics relations. The protocol also surfaces two methodology findings: LLM-judge reliability does not transfer across frameworks, and Stage 4 self-review is weak in every framework, with the model's own review wrongly reporting no earlier error in at least two-thirds of the trials that actually contained one. We release the full prompts, responses, verdicts, and audit records.