Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation

Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?

The transition probability in first-order perturbation theory for an Unruh-DeWitt detector coupled to a massless scalar field in Minkowski space is calculated. It has been shown recently that the conventional $iε$ regularisation prescription for the correlation function leads to non-Lorentz invariant results for the transition rate, and a different regularisation, involving spatial smearing of the field, has been advocated to replace it. We show that the non-Lorentz invariance arises solely from the assumption of sudden switch-on and switch-off of the detector, and that when the model includes…

Lorentz anomaly in the semi-light-cone gauge superstrings

We study the Lorentz invariance of D=4 and 6 superstrings in the double-spinor formalism, which are equivalent to the D=4 and 6 superstrings in the pure-spinor formalism in the sense of the BRST cohomology. We first re-examine how the conformal and Lorentz anomalies appear in the D=4 and 6 Green-Schwarz superstrings in the semi-light-cone gauge in the framework of BRST quantization. We construct a set of BRST invariant Lorentz generators and show that they do not form a closed algebra, even cohomologically. We then turn to the construction of Lorentz generators in the D=4 and 6 double-spinor s…

Why is High Energy Physics Lorentz Invariant?

Despite the tremendous empirical success of equivalence principle, there are several theoretical motivations for existence of a preferred reference frame (or aether) in a consistent theory of quantum gravity. However, if quantum gravity had a preferred reference frame, why would high energy processes enjoy such a high degree of Lorentz symmetry? While this is often considered as an argument against aether, here I provide three independent arguments for why perturbative unitarity (or weak coupling) of the Lorentz-violating effective field theories put stringent constraints on possible observabl…

Why the length of a quantum string cannot be Lorentz contracted

We propose a quantum gravity-extended form of the classical length contraction law obtained in Special Relativity. More specifically, the framework of our discussion is the UV self-complete theory of quantum gravity. Against this background, we show how our results are consistent with, i) the generalised form of the Uncertainty Principle (GUP), ii) the so called hoop-conjecture which we interpret, presently, as the saturation of a Lorentz boost by the formation of a black hole in a two-body scattering, and iii) the intriguing notion of "classicalization" of trans-Planckian physics. Pushing the…

Nilpotence varieties

We consider algebraic varieties canonically associated to any Lie superalgebra, and study them in detail for super-Poincaré algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of) the odd part of the algebra. Most of these varieties have appeared in various guises in previous literature, but we study them systematically here, from a new perspective: as the natural moduli spaces parameterizing twists of a super-Poincaré-invariant physical theory. We obtain a classification of all possible twists, as well as a systematic analysis of unbro…

$E=mc^2$ 与洛伦兹协变物理的对称性

$E=mc^2$ versus Symmetry for Lorentz Covariant Physics

本文探讨了$E=mc^2$与洛伦兹协变物理的对称性关系，质疑庞加莱对称性在相对论量子动力学中的基础地位，并提出了协变哈密顿动力学的新视角。