Letters in Mathematical Physics最新文献

Let (K_1 subset H) and (K_2 subset H) be half-sided modular inclusions in a common standard subspace H. We prove that the inclusion (K_1 subset K_2) holds if and only if we have an inclusion of spectral subspaces of the generators of the positive one-parameter groups associated to the half-sided modular inclusions (K_1 subset H) and (K_2 subset H). From this we give a characterization of this situation in terms of (operator-valued) symmetric inner functions. We illustrate these characterizations with some examples of non-trivial phenomena occurring in this setting.

A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct (Ntimes N) complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.

Compressible Navier–Stokes-Yukawa equations under stability condition (P'(bar{rho })+gamma bar{rho }>0) is considered, where P is the pressure, (bar{rho }) is the background density and the constant (gamma in mathbb {R}). We verify that the time-asymptotic shape of the solution contains a stationary diffusion wave superposing a moving diffusion wave with the propagation speed (sqrt{P'(bar{rho })+gamma bar{rho }}), which means that the sign of (gamma ) determines whether the potential fluid force enhances or deduces the propagation speed of the moving diffusion wave. This is completely different from the compressible Navier–Stokes-Poisson equations in Wang and Wu (2010JDE), where the Poisson potential critically impedes the speed of propagation wave such that pointwise description of the solution only contains a stationary diffusion wave. Besides, when (gamma =0), our pointwise result is consistent with the compressible Navier–Stokes equations in Liu and Wang (1998CMP).

We prove that the Kontsevich graph complex (textsf{GC}_d^{2}) and its oriented version (textsf{OGC}_{d+1}^2) are quasi-isomorphic as dg Lie algebras.

This paper intends to construct discrete spectral transformations for Cauchy–Jacobi orthogonal polynomials and to find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy–Jacobi orthogonal polynomials acts as the (tau )-function of the discrete CKP equation, which has been applied into Yang–Baxter equation, integrable geometry, cluster algebra, and so on.

The Fewster–Verch (FV) framework provides a local and covariant approach for defining measurements in quantum field theory (QFT). Within this framework, a probe QFT represents the measurement device, which, after interacting with the target QFT, undergoes an arbitrary local measurement. Remarkably, the FV framework is free from Sorkin-like causal paradoxes and robust enough to enable quantum state tomography. However, two open issues remain. First, it is unclear if the FV framework allows conducting arbitrary local measurements. Second, if the probe field is interpreted as physical and the FV framework as fundamental, then one must demand the probe measurement to be itself implementable within the framework. That would involve a new probe, which should also be subject to an FV measurement, and so on. It is unknown if there exist non-trivial FV measurements for which such an “FV-Heisenberg cut” can be moved arbitrarily far away. In this work, we advance the first problem by proving that Gaussian-modulated measurements of locally smeared fields fit within the FV framework. We solve the second problem by showing that any such measurement admits a movable FV-Heisenberg cut. As a technical by-product, we establish that state transformations induced by finite-rank perturbations of the classical phase space underlying a linear scalar field preserve the Hadamard property.

Nozaki et al. gave a homotopy classification of the knotted defects of ordered media in three-dimensional space by considering continuous maps from complements of spatial graphs to the order parameter space modulo a certain equivalence relation. We extend their result by giving a classification scheme for ordered media in handlebodies, where defects are allowed to reach the boundary. Through monodromies around meridional loops, global defects are described in terms of planar diagrams whose edges are colored by elements of the fundamental group of the order parameter space. We exhibit examples of this classification in octahedral frame fields and biaxial nematic liquid crystals.

Breathers have been experimentally and theoretically found in many physical systems—in particular, in integrable nonlinear-wave models. A relevant problem is to study the breather gas, which is the limit, for (Nrightarrow infty ), of N-breather solutions. In this paper, we investigate the breather gas in the framework of the focusing nonlinear Schrödinger (NLS) equation with nonzero boundary conditions, using the inverse scattering transform and Riemann–Hilbert problem. We address aggregate states in the form of N-breather solutions, when the respective discrete spectra are concentrated in specific domains. We show that the breather gas coagulates into a single-breather solution whose spectral eigenvalue is located at the center of the circle domain, and a multi-breather solution for the higher-degree quadrature concentration domain. These coagulation phenomena in the breather gas are called breather shielding. In particular, when the nonzero boundary conditions vanish, the breather gas reduces to an n-soliton solution. When the discrete eigenvalues are concentrated on a line, we derive the corresponding Riemann–Hilbert problem. When the discrete spectrum is uniformly distributed within an ellipse, it is equivalent to the case of the line domain. These results may be useful to design experiments with breathers in physical settings.

String-localized QFT allows to explain Standard Model interactions in an autonomous way, committed to quantum principles rather than a “gauge principle,” thus avoiding an indefinite state space and compensating ghosts. The resulting perturbative scattering matrix is known (at tree-level and without spacetime cutoff) to be insensitive to the non-locality of the auxiliary “string-localized free fields” used in the construction. For the examples of Yang–Mills and QCD, we prove that it is equivalent to the perturbative S-matrix of gauge theory, restricted to physical particle states. The role of classical gauge invariance is revealed along the way. The main tool are “dressed fields,” that are intermediate between free fields and interacting fields, and for which we give explicit formulas at all orders. The renormalization of loops, as well as non-perturbative issues are not addressed, but we hint at the possibility, enabled by our approach, that qualitative traces of confinement may be visible already at the level of the dressed fields.

We consider the homogeneous Bose gas in the three-dimensional unit torus, where N particles interact via a two-body potential of the form (N^{-1} v(x)). The system is studied at inverse temperatures of order (N^{-2/3}), which corresponds to the temperature scale of the Bose–Einstein condensation phase transition. We show that spontaneous U(1) symmetry breaking occurs if and only if the system exhibits Bose–Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.