Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
Quantum mechanics and the covariance of physical laws in quantum reference frames
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abstract
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a "superposition of coordinate transformations". We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.
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A new quantum deformation of the centrally extended Poincaré algebra is introduced whose universal T-matrix contracts to the Galilei T-matrix for quantum reference frames and appears as a central extension of the spacelike κ-Poincaré dual Hopf algebra.
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Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames
A new quantum deformation of the centrally extended Poincaré algebra is introduced whose universal T-matrix contracts to the Galilei T-matrix for quantum reference frames and appears as a central extension of the spacelike κ-Poincaré dual Hopf algebra.
- Indefinite probabilities in quantum spacetime: A deepening of unpredictability