Starting from a discussion of the concrete representations of the coordinates of the k-Minkowski spacetime (in 1+1 dimensions, for simplicity), we explicitly compute the associated Weyl operators as functions of a pair of Schroedinger operators. This allows for explicitly computing the trace of a quantised function of spacetime. Moreover, we show that in the classical (i.e. large scale) limit the origin of space is a topologically isolated point, so that the resulting classical spacetime is disconnected. Finally we show that there exist states with arbitrarily sharp simultaneous localisation in all the coordinates; in other words, an arbitrarily high energy density can be transferred to spacetime by means of localisation alone, which amounts to say that the model is not stable under localisation.
We study the limits to the localizability of events and reference frames in the $κ$-Minkowski quantum spacetime. Our main tool will be a representation of the $κ$-Minkowski commutation relations between coordinates, and the operator and measurement theory borrowed from ordinary quantum mechanics. Spacetime coordinates are described by operators on a Hilbert space, and a complete set of commuting observables cannot contain the radial coordinate and time at the same time. The transformation between the complete sets turns out to be the Mellin transform, which allows us to discuss the localizabil…
BPS Wilson loops in Minkowski spacetime and Euclidean space
我们给出了类空BPS威尔逊圈在闵可夫斯基时空中不存在的证据。我们证明了闵可夫斯基时空中的类空威尔逊圈不能保持任何超对称性，在$d = 4$ $\mathcal N = 4$ super Yang-Mills理论，$d = 3$ $\mathcal N = 2$ super Chern-Simons-matter理论和$d = 3$ $\mathcal N = 6$ Aharony-Bergman-Jafferis-Maldacena理论中。我们不仅使用无限的直线和圆作为例子来证明这一点，而且我们也给出了一般曲线的证明。我们把这归因于旋量的现实条件的冲突。然而，类空威尔逊圈确实存在于欧几里得空间中。存在沿无限直线的BPS威尔逊圈和圆形BPS威尔逊圈。这是因为在Wick旋转之后，旋量的现实条件消失了。从AdS/CFT对应关系来看，这一结果是合理的。
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to construct matrices of inner products which are then factored using the singular value decomposition to give coordinates in Minkowski spacetime. Results are presented showing good quality embeddings into Minkowski spacetime for dimensions d=2,3,4. The method applies in any dimension and does not require spacelike distances to be used as an input. It offers a new way …
Gravity is not only able to be mimicked in flat spacetimes, but also in curved spacetimes. We study analogue gravity models in curved spacetime by considering the relativistic Gross-Pitaevskii theory and Yang-Mills theory in the fixed background spacetime geometry. The results show that acoustic metrics can be emergent from curved spacetimes yielding a Hadamard product of a real metric-tensor and an analogue metric-tensor. Taking \emph{quantum vortices} as \emph{test particles}, we evaluate their released energy ratio during the "gravitational binding". The $2+1$-dimensional flat Minkowski met…
We consider the $\varrho$-Minkowski spacetime, a model with linear noncommutativity involving the time and the azimuthal angle. We study its quantum symmetries, the $\varrho$-Poincaré quantum group, and analyse the concepts of localizability and quantum observers.
Within any anticipated unifying theory of quantum gravity, it should be meaningful to combine the fundamental notions of quantum superposition and spacetime to obtain so-called "spacetime superpositions": that is, quantum superpositions of different spacetimes not related by a global coordinate transformation. Here we consider the quantum-gravitational effects produced by superpositions of periodically identified Minkowski spacetime (i.e.\ Minkowski spacetime with a periodic boundary condition) with different characteristic lengths. By coupling relativistic quantum matter to fields on such a s…
We compactify the ten-dimensional spacetime in heterotic supergravity leaving four-dimensional Minkowski spacetime. We search for nonsupersymmetric, non-Ricci-flat solutions of the equations of motion with the quadratic curvature term. By assuming that the extradimensional spaces are products of 2-manifolds, three types of solutions are found. They are $S^2\times T^2 \times H^2/Γ$, $S^2\times H^2/Γ\times H^2/Γ$, and $S^2\times S^2 \times H^2/Γ$, where $H^2/Γ$ denotes a compact hyperbolic manifold. The metrics can be written explicitly, and they can be applied to phenomenology.
We investigate the relation between the time-ordered vacuum correlation functions for interacting real scalar fields in Minkowski spacetime and in the Rindler wedge. The correlation functions are constructed perturbatively within the in-in formalism, often employed in calculations in more general spacetimes. We prove to all orders in perturbation theory that the time-ordered vacuum correlation functions can be calculated in the in-in formalism with internal vertices restricted to any Rindler wedge containing the external points. This implies that the Minkowski in-in (or in-out) perturbative ex…
Production of scalar particles by a relativistic, semi-transparent mirror in 1+3D Minkowski spacetime based on the Barton-Calogeracos (BC) action is investigated. The corresponding Bogoliubov coefficients are derived for a mirror with arbitrary trajectory. In particular, we apply our derived formula to the gravitational collapse trajectory. In addition, we identify the relation between the particle spectrum and the particle production probability, and we demonstrate the equivalence between our approach and the existing approach in the literature, which is restricted to 1+1D. In short, our trea…
