Let
be the
identity matrix and
. A matrix A is called symplectic if
. A symplectic matrix A is a commutator of symplectic involutions if
, where X and Y are symplectic matrices satisfying
. In this ...article, we give necessary and sufficient condition for a symplectic matrix over the complex number field to be expressed as a product of two commutators of symplectic involutions.
Averaged null energy condition from causality Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
The journal of high energy physics,
07/2017, Letnik:
2017, Številka:
7
Journal Article
Recenzirano
Odprti dostop
A
bstract
Unitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, ...we show that this implies that the averaged null energy,
∫ duT
uu
, must be non-negative. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to
n
-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form
∫ duX
uuu
···
u
≥ 0. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.
Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate ...nonequilibrium transport processes in a universal scaling regime and show how they lead to the breaking of the fluctuation-dissipation relation. As a consequence, the scaling of spectral functions (commutators) and statistical correlations (anticommutators) between different points in time and space become linearly independent with distinct dynamic scaling exponents. As a macroscopic signature of this phenomenon, we identify a transport peak in the statistical two-point correlator, which is absent in the spectral function showing the quasiparticle peaks of the Bose gas.
The spectrum of simplicial volume Heuer, Nicolaus; Löh, Clara
Inventiones mathematicae,
2021/1, Letnik:
223, Številka:
1
Journal Article
Recenzirano
Odprti dostop
New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes ...of orientable closed connected manifolds is dense in
R
≥
0
. In dimension 4 we prove that every non-negative rational number is the simplicial volume of some orientable closed connected 4-manifold. Our group theoretic results relate stable commutator length to the
l
1
-semi-norm of certain singular homology classes in degree 2. The output of these results is translated into manifold constructions using cross-products and Thom realisation.
A
bstract
All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D ...currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.
En este artículo se introduce algunas propiedades algebraicas de los subgrupoides y subgrupoides normales. Definimos el normalizador de un subgrupoide amplio H de un grupoide G y mostramos que, como ...en el caso de grupos, este normalizador es el mayor subgrupoide amplio de G en el cual H es normal. Además, damos las definiciones de centro Z(G) y conmutador G' del grupoide G y probamos que los dos son subgrupoides normales. También damos las nociones de isomorfismo interno e isomorfismo parcial de G y mostramos que el grupoide I(G) dado por el conjunto de todos los isomorfismos internos de G es un subgrupoide normal de A(G), el conjunto de todos los isomorfismos parciales de G. Además, probamos que I(G) es isomorfo al grupoide cociente G/Z(G), lo cual extiende a grupoides un resultado bien conocido para grupos.
An RD-space \(\mathcal{X}\) is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in \(\mathcal{X}\). In this setting, ...the authors establish the boundedness of bilinear \(\theta\)-type Calderón-Zygmund operator \(T_{\theta}\) and its commutator \(b_1,b_2,T_{\theta}\) generated by the function \(b_1,b_2\in BMO(\mu)\) and \(T_{\theta}\) on generalized weighted Morrey space \(\mathcal{M}^{p,\phi}(\omega)\) and generalized weighted weak Morrey space \(W\mathcal{M}^{p,\phi}(\omega)\) over RD-spaces.
PDF
