Quantum conformal symmetries for spacetimes in superposition

Abstract

Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension of the quantum reference frame formalism to address this question for the Klein-Gordon field residing on a superposition of conformally equivalent metrics. Based on the group structure of ``quantum conformal transformations'', we construct an explicit quantum operator that can map states describing a quantum field on a superposition of spacetimes to states representing a quantum field with a superposition of masses on a Minkowski background. This constitutes an extended symmetry principle, namely invariance under quantum conformal transformations. The latter allows to build an understanding of superpositions of diffeomorphically non-equivalent spacetimes by relating them to a more intuitive superposition of quantum fields on curved spacetime. Furthermore, it can be used to import the phenomenon of particle production in curved spacetime to its conformally equivalent counterpart, thus revealing new features in modified Minkowski spacetime.

arXiv comment13+4 pages, 4 figures. v3: version accepted in Quantum. Comments are welcome

References in corpus (29)

• Analogue Gravity
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Universal decoherence due to gravitational time dilation
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• Quantum interferometric visibility as a witness of general relativistic proper time
• The Trinity of Relational Quantum Dynamics
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• Cosmological Particle Production: A Review
• Quantum field theory on a cosmological, quantum space-time
• Bell's Theorem for Temporal Order
• Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
• Physics within a quantum reference frame
• Quantum superposition of spacetimes obeys Einstein's Equivalence Principle
• Quantum reference frames for general symmetry groups
• Relativistic quantum reference frames: the operational meaning of spin
• Entanglement of quantum clocks through gravity
• Spacetime Quantum Reference Frames and superpositions of proper times
• Massive Klein--Gordon equation from a BEC-based analogue spacetime
• Quantized fields and gravitational particle creation in f(R) expanding universes
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Quantum signatures of black hole mass superpositions
• Kinematics and dynamics in noninertial quantum frames of reference
• Schrödinger's cat for de Sitter spacetime
• Transformation of Spin in Quantum Reference Frames
• Quantum reference frames for an indefinite metric
• A new symmetry of the relativistic wave equation
• Entanglement-asymmetry correspondence for internal quantum reference frames
• Quantum generalisation of Einstein's Equivalence Principle can be verified with entangled clocks as quantum reference frames
• Schrödinger's Black Hole Cat

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• Space-time superpositions as fluctuating geometries
• Quantum Galilei group as quantum reference frame transformations
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks