Letters in Mathematical Physics最新文献

We investigate the capability of symplectic quandles to detect causality for (2+1)-dimensional globally hyperbolic spacetimes (X). Allen and Swenberg showed that the Alexander–Conway polynomial is insufficient to distinguish connected sum of two Hopf links from the links in the family of Allen–Swenberg 2-sky like links, suggesting that it cannot always detect causality in X. We find that symplectic quandles, combined with Alexander–Conway polynomial, can distinguish these two types of links, thereby suggesting their ability to detect causality in X. The fact that symplectic quandles can capture causality in the Allen–Swenberg example is intriguing since the theorem of Chernov and Nemirovski, which states that Legendrian linking equals causality, is proved using Contact Geometry methods.

We consider topological twists of four-dimensional (mathcal {N}=2) supersymmetric QCD with gauge group SU(2) and (N_fle 3) fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which provides an infinite family of topological partition functions. In this Part I, we demonstrate that in the presence of such fluxes the theories can be formulated for arbitrary gauge bundles on a compact four-manifold. Moreover, we consider arbitrary masses for the hypermultiplets, which introduce new intricacies for the evaluation of the low-energy path integral on the Coulomb branch. We develop techniques for the evaluation of these path integrals. In the forthcoming Part II, we will deal with the explicit evaluation.

A Landau–Zener-type formula for a degenerate avoided-crossing is studied in the non-coupled regime. More precisely, a (2times 2) system of first-order h-differential operator with (mathcal {O}(varepsilon )) off-diagonal part is considered in 1D. Asymptotic behavior as (varepsilon h^{m/(m+1)}rightarrow 0^+) of the local scattering matrix near an avoided-crossing is given, where m stands for the contact order of two curves of the characteristic set. A generalization including the cases with vanishing off-diagonals and non-Hermitian symbols is also given.

We define the (frac{{{mathbb {Z}}}}{2})-graded meromorphic open-string vertex algebra that is an appropriate noncommutative generalization of the vertex operator superalgebra. We also illustrate an example that can be viewed as a noncommutative generalization of the free fermion vertex operator superalgebra. The example is built upon a universal half-integer-graded non-anti-commutative Fock space where a creation operator and an annihilation operator satisfy the fermionic anti-commutativity relation, while no relations exist among the creation operators. The former feature allows us to define the normal ordering, while the latter feature allows us to describe interactions among the fermions. With respect to the normal ordering, Wick’s theorem holds and leads to a proof of weak associativity and a closed formula of correlation functions.

Impulsive gravitational waves are theoretical models of short but violent bursts of gravitational radiation. They are commonly described by two distinct spacetime metrics, one of local Lipschitz regularity and the other one even distributional. These two metrics are thought to be ‘physically equivalent’ since they can be formally related by a ‘discontinuous coordinate transformation’. In this paper we provide a mathematical analysis of this issue for the entire class of nonexpanding impulsive gravitational waves propagating in a background spacetime of constant curvature. We devise a natural geometric regularisation procedure to show that the notorious change of variables arises as the distributional limit of a family of smooth coordinate transformations. In other words, we establish that both spacetimes arise as distributional limits of a smooth sandwich wave taken in different coordinate systems which are diffeomorphically related.

In this letter, we obtain the precise range of the values of the parameter (alpha ) such that Petz–Rényi (alpha )-relative entropy (D_{alpha }(rho ||sigma )) of two faithful displaced thermal states is finite. More precisely, we prove that, given two displaced thermal states (rho ) and (sigma ) with inverse temperature parameters (r_1, r_2,ldots , r_n) and (s_1,s_2, ldots , s_n), respectively, (0<r_j,s_j<infty ), for all j, we have

where we adopt the convention that the minimum of an empty set is equal to infinity. This result is particularly useful in the light of operational interpretations of the Petz–Rényi (alpha )-relative entropy in the regime (alpha >1 ). Along the way, we also prove a special case of a conjecture of Seshadreesan et al. (J Math Phys 59(7):072204, 2018. https://doi.org/10.1063/1.5007167).

In this paper, we present the connection of two concepts as induced representation and partially reduced irreducible representations (PRIR) appear in the context of port-based teleportation protocols. Namely, for a given finite group G with arbitrary subgroup H, we consider a particular case of matrix irreducible representations, whose restriction to the subgroup H, as a matrix representation of H, is completely reduced to diagonal block form with an irreducible representation of H in the blocks. The basic properties of such representations are given. Then as an application of this concept, we show that the spectrum of the port-based teleportation operator acting on n systems is connected in a very simple way with the spectrum of the corresponding Jucys–Murphy operator for the symmetric group (S(n-1)subset S(n)). This shows on the technical level relation between teleporation and one of the basic objects from the point of view of the representation theory of the symmetric group. This shows a deep connection between the central object describing properties of deterministic PBT schemes and objects appearing naturally in the abstract representation theory of the symmetric group. In particular, we present a new expression for the eigenvalues of the Jucys–Murphy operators based on the irreducible characters of the symmetric group. As an additional but not trivial result, we give also purely matrix proof of the Frobenius reciprocity theorem for characters with explicit construction of the unitary matrix that realizes the reduction in the natural basis of induced representation to the reduced one.

The main purpose of this paper is to discuss the Cauchy problem of integrable nonlocal (reverse-space-time) Kundu–Eckhaus (KE) equation through the Riemann–Hilbert (RH) method. Firstly, based on the zero-curvature equation, we present an integrable nonlocal KE equation and its Lax pair. Then, we discuss the properties of eigenfunctions and scattering matrix, such as analyticity, asymptotic behavior, and symmetry. Finally, for the prescribed step-like initial value: (u(z,t)=o(1)), (zrightarrow -infty ) and (u(z,t)=R+o(1)), (zrightarrow +infty ), where (R>0) is an arbitrary constant, we consider the initial value problem of the nonlocal KE equation. The paramount techniques is the asymptotic analysis of the associated RH problem.

We provide a simple method to recognize a classical orthogonal polynomial sequence on a q-quadratic lattice defined only by the three-term recurrence relation. It is pointed out that this can be extended to all orthogonal polynomials in the q-Askey scheme.