Conformal quantum mechanics of causal diamonds

Abstract

It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors one finds a class which maps causal diamonds in Minkowski space-time into themselves. The flow of such Killing vectors describes worldlines of accelerated observers with a finite lifetime within the causal diamond. Time evolution of static diamond observers is equivalent to time evolution in conformal quantum mechanics governed by a hyperbolic Hamiltonian and covering only a segment of the time axis. This indicates that the Unruh temperature perceived by static diamond observers in the vacuum state of inertial observers in Minkowski space can be obtained from the behaviour of the two-point functions of conformal quantum mechanics.

13 pages, no figures

References in corpus (4)

• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• Conformal mapping of Unruh temperature
• The Geometry of Large Causal Diamonds and the No Hair Property of Asymptotically de-Sitter Spacetimes
• Remarks on Rindler Quantization

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• Thermal effect in a causal diamond: open quantum systems approach
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• Vacuum thermal effects in flat space-time from conformal quantum mechanics
• Physical Representations of Corner Symmetries
• A Modular Operator Approach to Entanglement of Causally Closed Regions
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
• Thermodynamics as a tool for (quantum) gravitational dynamics
• Horizon brightened acceleration radiation entropy in causal diamond geometry: A near-horizon perspective
• Path integral derivation of the thermofield double state in causal diamonds
• From spacetime thermodynamics to Weyl transverse gravity
• Superpositions of thermalisations in relativistic quantum field theory
• The Cosmological Constant from Conformal Transformations: Möbius Invariance and Schwarzian Action
• Thermal nature of the causal diamond horizon: A hidden property of the inertial propagator
• Modular theory and affine representations on the Rindler horizon
• Thermodynamics of spacetime from minimal area