Letters in Mathematical Physics最新文献

We report a rigorous quantization of topological quantum mechanics on (mathbb {R}_{geqslant 0}) and (textbf{I}= [0, 1]) in the perturbative BV-BFV formalism. Costello’s homotopic renormalization is extended and incorporated in our construction. As a consequence, we obtain an algebraic characterization of the solutions to the modified quantum master equation. In addition, BV quantization of the same model studied in previous work (Wang and Yan 2022) is derived from the BV-BFV quantization, leading to a comparison between two different frameworks in the study of quantum field theories on manifolds with boundaries.

We introduce L-functions attached to negative-definite plumbed manifolds as the Mellin transforms of homological blocks. We prove that they are entire functions and their values at ( s=0 ) are equal to the Witten–Reshetikhin–Turaev invariants by using asymptotic techniques developed by the author in the previous papers. We also prove linear relations between special values at negative integers of some L-functions, which are common generalizations of Hurwitz zeta functions, Barnes zeta functions and Epstein zeta functions.

Using the free fermions technique and bosonization rules, we introduce the multicomponent DKP hierarchy as a generating bilinear integral equation for the tau-function. A number of bilinear equations of the Hirota–Miwa type are obtained as its corollaries. We also consider the dispersionless version of the hierarchy as a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the F-function). We show that there is an elliptic curve built in the structure of the hierarchy, with the elliptic modulus being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization many dispersionless equations of the Hirota–Miwa type become equivalent to a single equation having a nice form.

We construct a Lorentzian length space with an orthogonal splitting on a product (Itimes X) of an interval and a metric space and use this framework to consider the relationship between metric and causal geometry, as well as synthetic time-like Ricci curvature bounds. The generalized Lorentzian product carries a natural Lorentzian length structure but can fail the push-up condition in general. We recover the push-up property under a log-Lipschitz condition on the time variable and establish sufficient conditions for global hyperbolicity. Moreover, we formulate time-like Ricci curvature bounds without push-up and regularity assumptions and obtain a partial rigidity of the splitting under a strong energy condition.

We explore a ({mathfrak {gl}}_{r})-covariant parameterisation of Bethe algebra appearing in ({mathfrak {so}}_{2r}) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.

We prove that the intrinsic geometry of compact cross sections of an extremal horizon in four-dimensional Einstein–Maxwell theory must admit a Killing vector field or is static. This implies that any such horizon must be an extremal Kerr–Newman horizon and completes the classification of the associated near-horizon geometries. The same results hold with a cosmological constant.

The computation of scattering amplitudes in the presence of non-trivial background gauge fields is an important but extremely difficult problem in quantum field theory. In even the simplest backgrounds, obtaining explicit formulae for processes involving more than a few external particles is often intractable. Recently, it has been shown that remarkable progress can be made by considering background fields which are chiral in nature. In this paper, we obtain a compact expression for the tree-level, maximal helicity violating (MHV) scattering amplitude of an arbitrary number of gluons in the background of a self-dual dyon. This is a Cartan-valued, complex gauge field sourced by a point particle with equal electric and magnetic charges and can be viewed as the self-dual version of a Coulomb field. Twistor theory enables us to manifest the underlying integrability of the self-dual dyon, trivializing the perturbative expansion in the MHV sector. The formula contains a single position-space integral over a spatial slice, which can be evaluated explicitly in simple cases. As an application of the formula, we show that the holomorphic collinear splitting functions of gluons in the self-dual dyon background are un-deformed from a trivial background, meaning that holomorphic celestial OPE coefficients and the associated chiral algebra are similarly un-deformed. We also comment on extensions of our MHV formula to the full tree-level gluon S-matrix.

We revisit key notions related to the evolution of quantum information in few-body quantum mechanics (fbQM) and, for a wide class of dispersion relations, prove uniform bounds on the maximal speed of propagation of quantum information for states and observables with exponential error bounds. Our results imply, in particular, a fbQM version of the Lieb–Robinson bound, which is known to have wide applications in quantum information sciences. We propose a novel approach to proving maximal speed bounds.

It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms between Cauchy surfaces arise naturally in the context of algebraic quantum field theory. The underlying functorial field theory encodes the time evolution of the original theory, but not its spatially local structure. As an illustrative application of these results, the algebraic and functorial descriptions of a free scalar quantum field are compared in detail.

We undertake a detailed study of the gaugings of two-dimensional Yang–Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the meaning of dual lower form symmetries. Our derivations of orbifold gauge theories make use of a combination of standard continuum path integral methods, networks of topological defects, and techniques from higher gauge theory. We provide a unified description of higher and lower form gauge fields for a p-form symmetry in the geometric setting of p-gerbes, and derive reverse orbifolds by the dual ((-1))-form symmetries. We identify those orbifolds in which charge conjugation symmetry is spontaneously broken, and relate the breaking to mixed anomalies involving ((-1))-form symmetries. We extend these considerations to gaugings by the non-invertible 1-form symmetries of two-dimensional Yang–Mills theory by introducing a notion of generalized (theta )-angle.