Letters in Mathematical Physics最新文献

We give a q-analogue of Howe duality associated with a pair ((mathfrak {g},G)), where (mathfrak {g}) is an orthosymplectic Lie superalgebra and (G=O_ell , Sp_{2ell }). We define explicitly commuting actions of a quantized enveloping algebra of (mathfrak {g}) and the (imath )quantum group of types AI and AII on a q-deformed supersymmetric space, and describe its semisimple decomposition whose classical limit recovers the ((mathfrak {g},G))-duality. As special cases, we obtain q-analogues of ((mathfrak {g},G))-dualities on symmetric and exterior algebras for (mathfrak {g}=mathfrak {so}_{2n}), (mathfrak {sp}_{2n}).

We introduce a family of 3d (mathcal {N}=4) superconformal field theories that have zero-dimensional Coulomb and Higgs branches and propose that the rational vertex operator algebras (W^{text{ min }}_{k - scriptstyle {frac{1}{2}}}(mathfrak {sp}_{2N})) and (L_{k}(mathfrak {osp}_{1|2N})) model the modular tensor categories of line operators in their topological A and B twists, respectively. Our analysis indicates that the action of 3d mirror symmetry on this family of theories is related to a novel level-rank duality and leads to several conjectural q-series identities of independent interest.

This paper is concerned with the global existence and blowup of the classical solution to the Cauchy problem of the relativistic Euler equation with ( p=0 ) in a fixed Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. The aim of this work is to study clearly the effect of the expansion rate of the spacetime on the life span of the classical solution to the pressureless fluid. Since the density and the velocity of the relativistic dust admit the same principal part, we can obtain much more accurate results by the characteristic method rather than energy estimates.

Previously introduced the (GL_{ell +1}(mathbb {R})) Hecke–Baxter operator is a one-parameter family of elements in the commutative spherical Hecke algebra (mathcal {H}(GL_{ell +1}(mathbb {R}),O_{ell +1})). Its action on spherical vectors in spherical principal series representations of (GL_{ell +1}(mathbb {R})) is given by multiplication by the Archimedean L-factors associated with these representations. In this note, we propose an extension of the construction to other (non-spherical) (GL_{ell +1}(mathbb {R})) principal series representations providing a relevant generalization of the notions of spherical vector, commutative spherical Hecke algebra and the Hecke–Baxter operator to the general case. Action of the introduced Hecke–Baxter operator on the generalized spherical vectors is given by multiplication by the Archimedean L-factor associated with the corresponding principal series representation of (GL_{ell +1}(mathbb {R})).

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.