相关论文: The Necessity of the Hadamard Condition

The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…

The Hadamard parametrix is a representation of the short-distance singularity structure of the Feynman Green's function for a quantum field on a curved space-time background. Subtracting these divergent terms regularizes the Feynman Green's…

We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables…

In this paper, we study a free scalar field in a specific (1+1)-dimensional curved spacetime. By introducing an algebraic state that is locally Hadamard, we derive the renormalized Wightman function and explicitly calculate the covariantly…

The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in…

It has been shown recently that a nonrelativistic quantum particle constrained to a hard-wall layer of constant width built over a geodesically complete simply connected noncompact curved surface can have bound states provided the surface…

Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a non-negative effective energy density (EED). The SEC ensures the timelike convergence property. However,…

We are concerned with the existence of ground states for nonlinear Choquard equations involving a critical nonlinearity in the sense of Hardy-Littlewood-Sobolev. Our result complements previous results by Moroz and Van Schaftingen where the…

Having in mind present uncertainty of the experimental situation in respect to exotic hadrons, it is important to discuss any possible theoretical arguments, pro and contra. Up to now, there are no theoretical ideas which could forbid…

The vanishing of the divergence of the total stress tensor (magnetic plus kinetic) in a neighborhood of an equilibrium plasma containing a toroidal surface of discontinuity gives boundary and jump conditions that strongly constrain…

We consider real scalar field theories whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential $V$. By means of an extension of the standard definition of M{\o}ller operator, we construct an isomorphism…

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a…

This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…

We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…

In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…

The Wightman two-point function of any Hadamard state of a linear quantum field theory determines a corresponding Feynman propagator. Conversely, however, a Feynman propagator determines a state only if certain positivity conditions are…

In quantum field theory in curved spacetimes the construction of the algebra of observables of linear fields is today well understood. However, it remains a non-trivial task to construct physically meaningful states on the algebra. For…

Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…

In a recent paper (Phys. Rev. D 94, 125016 (2016)), the authors argued that the singularities of the two-point functions on the Poincar\'e domain of the $n$-dimensional anti-de Sitter spacetime ($\text{PAdS}_n$) have the Hadamard form,…

Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is…