Quantum field theory treatment of oscillations of Dirac neutrinos in external fields

Large Language Models (LLMs) can make nontrivial contributions to math and physics, if used properly. Separate model instances used to Generate and Verify research steps produce more reliable results than single-shot inference. As a specific example, I describe the use of AI in recent research in quantum field theory (Tomonaga–Schwinger integrability conditions applied to state-dependent modifications of quantum mechanics), work now accepted for publication in Physics Letters B after peer review. Remarkably, the main idea in the paper originated de novo from GPT-5. GPT-5, Gemini and Qwen-Max were used extensively to perform calculations, find errors and generate the finished paper.

A bstract Quantum sinh-Gordon model in 1 + 1 dimensions is one of the simplest and best-studied massive integrable relativistic quantum field theories. We consider this theory on a multi-sheeted Riemann surfaces with a flat metric, which can be seen as a pile of planes connected to each other along cut lines. The cut lines end at branch points, which are represented by a twist operator $$ {\mathcal{T}}_n $$ T n . Operators of such kind are interesting in the framework of the problem of computing von Neumann and Renyi entanglement entropies in the original model on the plane. The composite branch-point twist operators (CTO) are a natural generalization of the twist operators, obtained by placing a local operator to a branch point by means of a certain limiting procedure. Correlation function in quantum field theory can be, in principle, found by means of the spectral decomposition. It allows one to express them in terms of form factors of local operators, i.e. their matrix elements in the basis of stationary states. In integrable models complete sets of exact form factors of all operators can be found exactly as solutions of a system of bootstrap equations. Nevertheless, identification of these solution to the operators in terms of the basic fields remains problematic. In this work, we develop a technique of computing form factors of a class of CTO determined in terms of the basic field in the semiclassical approximation.

This second Special Issue on Quantum Field Theory is a continuation of the first Special Issue on quantum field theory [...]

The Yang-Baxter equation is a famous equation in mathematics and mathematical physics. It plays a central role in several areas of mathematics, including algebra, topology, and quantum field theory. The aim of the workshop is to review recent developments in areas where the Yang-Baxter equation is crucial to discuss new research directions and ideas for addressing open problems.

Abstract This paper offers a historical overview of the origins and enduring significance of gravitational particle creation, a groundbreaking discovery first formulated in Leonard Parker’s 1966 doctoral thesis at Harvard University. By tracing the context in which Parker developed this idea and examining its subsequent influence, the paper highlights how the concept of gravitational particle creation advanced the study of quantum field theory in curved spacetime and profoundly shaped modern cosmology, as well as the quantum theory of black holes.

A bstract The measurement of the anomalous electron magnetic moment g – 2 through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this “cavity shift” must subtract the electron’s divergent self-field, and thus require knowledge of the exact Green’s function for the cavity’s electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.

We derive the energy-differential cross section and energy loss rate for dissipative self-interacting dark matter (dSIDM) models within the Born regime using perturbative quantum field theory. Six dissipative scenarios are considered, incorporating the emission of particles that may be either massless or possess a kinematically allowed light mass. Both short-range and long-range force-mediated dSIDM interactions are examined. In the non-relativistic regime, we obtain closed-form expressions of the energy-differential cross sections by a controlled expansion in the initial relative dark matter velocity. Up to trivial factors, the leading-order squared emission amplitude is model-independent for massless emissions. Model dependence arises for massive particle emission and at the next-to-leading order. The latter reduces to three distinct cases. The derived analytical expressions exhibit excellent agreement with numerical computations, providing simple, ready-to-use formulas. Furthermore, we analyze the behavior of these processes in the soft emission limit. Our results show that additional corrections are necessary when applying factorization at the next-to-leading order in a velocity expansion to ensure consistency between the soft energy-differential cross section and the full counterparts across a broad energy range. Finally, we investigate the regime of perturbative validity in terms of the model parameters, identifying the conditions under which our results are applicable.

Clifford quantum cellular automata from topological quantum field theories and invertible subalgebras

Abstract The Casimir effect, a fundamental manifestation of quantum vacuum fluctuations, has evolved from a curiosity between idealized metallic plates to a versatile probe of quantum and material properties in structured and time-dependent media. This review traces the progression of Casimir force research from its classical formulation in noble metals like gold (Au) to cutting-edge developments involving metamaterials and time crystals. Beyond surveying recent experimental and theoretical advances, we provide a unifying framework that bridges Casimir physics with essential solid-state principles—including band theory, dielectric response, and temporal periodicity—critical for understanding forces in real and engineered materials. Special attention is given to non-equilibrium and dynamically modulated systems, where time-periodic structures can profoundly alter vacuum-induced interactions. By synthesizing insights from quantum field theory and condensed matter physics, this review offers a comprehensive perspective on the rich interplay between quantum fluctuations, material response, and temporal symmetry breaking.

A bstract We study Krylov complexity in Schrödinger field theory in the grand canonical ensemble with chemical potential μ , with an emphasis on the qualitatively new features that arise for μ > 0. In this regime the fermionic Wightman power spectrum is effectively single-sided and sharply truncated at ω = μ , which induces a crossover in the Lanczos coefficients and signals a dynamical transition from a bulk-dominated regime to a spectral-edge-dominated regime: b n displays a two-stage linear growth (from an early-time slope π/β to an asymptotic slope 2 /β ), while a n bends from near-zero values to a linear descent with slope −4 /β . We provide analytic support for the resulting complexity growth from three complementary viewpoints: (i) using an SL(2 , ℝ) algebraic construction matched to the asymptotic Lanczos data, we show that the late-time Krylov complexity must grow quadratically, K ( t ) ∝ t 2 ; (ii) by analyzing engineered Wightman spectra with controlled decay and truncation, we identify single-sided exponential decay as the key spectral feature responsible for the quadratic asymptotics, while an approximately even two-sided exponential spectrum explains the early-time K ( t ) ~ sinh 2 ( πt/β ) behavior at large μ ; (iii) we formulate the problem in terms of orthogonal polynomials and estimate the crossover scale separating the early- and late-stage regimes. Overall, our results help clarify the role of chemical potential and spectral truncation in shaping operator growth and Krylov complexity in this non-relativistic quantum field theory setting.

A bstract We develop a perturbative understanding of the modular Hamiltonian for a 2D CFT, divided into left and right half-spaces, with a weak local perturbation inserted in the future wedge. A formal perturbation series for the modular Hamiltonian is available, but must be properly interpreted in quantum field theory. We work inside correlation functions with spectator operators, and introduce a prescription for defining complex modular flow via analytic continuation to properly resolve singularities. From the correlators, we extract an operator expression for the modular Hamiltonian. It takes the form of a local operator in the future wedge plus contact terms with an unconventional singularity structure. Thanks to this structure the KMS conditions are satisfied, which independently establishes the validity of the results. Similar techniques apply to perturbations inserted in the past wedge. We mention various future directions, including an all-orders speculation for the excited state modular Hamiltonian.

A bstract The states of a single photon in four-dimensional de Sitter (dS) spacetime form a Unitary Irreducible Representation (UIR) of SO(1,4), which we call the photon UIR. While in flat spacetime photons are intimately tied to gauge symmetry, we demonstrate that in de Sitter, photon states emerge generically in any quantum field theory, even without an underlying U(1) gauge field. We derive a Källén-Lehmann representation for antisymmetric tensor two-point functions and show that numerous composite operators constructed from massive free fields can create states in the photon UIR. Remarkably, we find that some of these operators exhibit two-point functions with slower late-time and large-distance decay than the electromagnetic field strength itself, challenging the conventional notion that photons dominate the infrared regime. Using our spectral representation, we establish non-perturbative bounds on the late-time behavior of electric and magnetic fields in de Sitter, with potential implications for primordial magnetogenesis. Through one-loop calculations, we demonstrate that both the creation of photon states and the enhanced late-time large-distance behavior persist in weakly interacting theories.

The brain biofield, which represents the electromagnetic field generated by neurons, is hypothesized to play a role in neural communication, potentially complementing well-established, relatively slow chemical signaling and relatively fast conventional electrical signaling. Evidence was recently provided that neurons, and even entire nervous tissue, emit ultra-weak photons known as biophotons. From the perspective of quantum field theory, field particles, such as photons, act as universal mediators of interactions between matter particles, including electrons. When considering such a principle extended across scales from atoms to biomolecules, cells, and even whole tissues, biophotons might mediate ultrafast interactions between neurons occurring at the speed of light. Specific quantum properties of photons, such as superposition, coherence, and entanglement, could provide a physical basis for biophoton-mediated communication. However, neither the formation of such a quantum state associated with information coding nor its detection associated with decoding has yet been experimentally demonstrated in neural tissue. Furthermore, the stable propagation of a quantum state is severely limited by inherent biological noise, including thermal, chemical, and structural fluctuations, which rapidly destabilize the quantum state in neural tissue. Thus, biofield-mediated communication in the brain remains largely hypothetical and requires substantial experimental investigation before its feasibility can be assessed. Although direct experimental evidence remains limited, biophoton-mediated signaling represents a promising frontier for understanding neural communication within a quantum framework. Recent advances in biophoton detection might open new opportunities to investigate the role of biophotons in neural communication.

A bstract In the presence of ’t Hooft anomalies, backgrounds for the symmetries of a quantum field theory can lead to non-conservation of Noether currents, or more generally, to the presence of charged insertions in the path integral. When there is a net background charge, the partition function evaluated on closed manifolds will vanish. For anomalous symmetries, this statement can also be understood as the anomaly theory giving rise to a non-trivial anomalous phase for the partition function even for “rigid” transformations which leave all background fields unchanged. We use the generalisation of this second viewpoint to the setting of anomalous higher-form symmetries in order to show vanishing of the partition function for a number of examples, both with and without a Lagrangian description. In particular, we show how to derive from these considerations the analogue of the Freed-Witten anomaly cancellation condition for the M5-brane, and also that for the D3-brane in S-fold backgrounds.

A bstract In this work, we compute the anomalous dimensions of the ϕ Q operator in six-dimensional cubic scalar theory. The renormalization analysis is carried out within the framework of the Operator Product Expansion method, while the ultraviolet divergences of Feynman integrals are evaluated using the graphical function method. Inspired by the intrinsic connection between Wilson coefficients and anomalous dimensions, an algorithm was proposed recently, which provides a practical and systematic framework for calculating the anomalous dimensions of masses, fields, and composite operators, with broad potential applicability to generic quantum field theories. Notably, the HyperlogProcedures package, developed based on the graphical function method, enables the computation of two-point propagator-type integrals, derived herein for capturing ultraviolet divergences, to very high loop orders. With these advanced techniques, we have successfully computed the anomalous dimensions of the ϕ Q operator up to five loops. Furthermore, we present a large N expansion of the scaling dimensions at the Wilson-Fisher fixed point, extended to the 1 /N 5 order. This computation sets a new loop-order record for the anomalous dimension of the ϕ Q operator in cubic scalar theory, while further validating the efficiency and versatility of the proposed algorithm in renormalization analyses.

Abstract We provide a mathematically rigorous Keldysh functional integral for fermionic quantum field theories. We show convergence of a discrete-time Grassmann Gaussian integral representation in the time-continuum limit under very general hypotheses. We also prove analyticity of the effective action and explicit bounds for the truncated (connected) expectation values $$\gamma ^\textrm{c}_{m,\bar{m}}$$ γ m , m ¯ c of the non-equilibrium system. These bounds imply clustering with a summable decay in the thermodynamic limit, provided these properties hold at time zero, and provided that the determinant bound $$\delta _C$$ δ C and decay constant $$\alpha _C$$ α C of the fermionic Keldysh covariance are bounded uniformly in the volume. We then give bounds for these constants and show that uniformity in the volume indeed holds for a general class of systems. Finally we show that in the setting of dissipative quantum systems, these bounds are not necessarily restricted to short times.

Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach [L. Bhardwaj et al., SciPost Phys. 19, 056 (2025); L. Bhardwaj et al., arXiv: 2502.20440]. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider “all-boson type” fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups G G (possibly with an ’t Hooft anomaly) via generalized gauging—that is, by stacking with an H H -symmetric TFT and gauging a subgroup H H . The continuum classification directly informs the lattice data, such as the generalized gauging that determines the symmetry category, and the data that specifies the gapped phase. We construct commuting projector Hamiltonians and ground states applicable to any non-chiral gapped phase with such symmetries. We also describe the ground states in terms of tensor networks. In light of the length of the paper, we include a self-contained summary section presenting the main results and examples.

A bstract We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by taking derivatives of this path integral with respect to the boundary values. The S-matrix of the QFT can be extracted directly from these boundary correlation functions after smearing. We interpret this relation in terms of coherent state quantization and derive the constraints on the path-integral as a function of boundary values that follow from the unitarity of the S-matrix. We then study the locality structure of boundary correlation functions. In the massive case, we find that the boundary correlation functions for generic locations of boundary points are dominated by a saddle point which has the interpretation of particles scattering in a small elevator in the bulk, where the location of the elevator is determined dynamically, and the S-matrix can be recovered after stripping off some dynamically determined but non-local “renormalization” factors. In the massless case, we find that while the boundary correlation functions are generically analytic as a function on the whole manifold of locations of boundary points, they have special singularities on a sub-manifold, points on which correspond to light-like scattering in the bulk. We completely characterize this singular scattering sub-manifold, and find that the corresponding residues of the boundary correlations at these singularities are precisely given by S-matrices. This analysis parallels the analysis of bulk-point singularities in AdS/CFT and generalizes it to the case of multi-bulk point singularities.

In this work, we investigate massive charged scalar perturbations in the background of three-dimensional dilaton black holes with a cosmological constant. We demonstrate that the wave equations governing the dynamics of these perturbations are exactly solvable, with the radial part expressible in terms of confluent Heun functions. The quasibound state frequencies are computed analytically, and we examine their dependence on the scalar field’s mass and charge, as well as on the black hole’s mass and electric charge. Our analysis also underscores the crucial role played by the cosmological constant in shaping the behavior of these perturbations. This specific black hole metric arises as a solution to the low-energy effective action of string theory in 2+1 dimensions, and it holds potential for experimental realization in analog gravity systems due to the similarity between its surface gravity and that of acoustic analogs. Moreover, the analytic tractability of this system offers a valuable testing ground for exploring aspects of black hole spectroscopy, stability, and quantum field theory in curved spacetime. The exact solvability facilitates deeper insights into the interplay between geometry and matter fields in lower-dimensional gravity, where quantum gravitational effects can be more pronounced. Such studies not only enrich our understanding of dilaton gravity and its string-theoretic implications but also pave the way for potential applications in simulating black hole phenomena in laboratory settings using analog models.