A ground state for the causal diamond in 2 dimensions
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We apply a recent proposal for a distinguished ground state of a quantum field in a globally hyperbolic spacetime to the free massless scalar field in a causal diamond in two-dimensional Minkowski space. We investigate the two limits in which the Wightman function is evaluated (i) for pairs of points that lie in the centre of the diamond (i.e. far from the boundaries), and (ii) for pairs of points that are close to the left or right corner. We find that in the centre, the Minkowski vacuum state is recovered, with a definite value of the infrared cutoff. Interestingly, the ground state is not the Rindler vacuum in the corner of the diamond, as might have been expected, but is instead the vacuum of a flat space in the presence of a static mirror on that corner. We confirm these results by numerically evaluating the Wightman function of a massless scalar field on a causal set corresponding to the continuum causal diamond.
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- A ground state for the causal diamond in 2 dimensions
Journal of High Energy Physics
- Online Date
- October 2012
- Online ISSN
- Additional Links
- Field Theories in Lower Dimensions
- Nonperturbative Effects
- Lattice Quantum Field Theory
- Stochastic Processes
- Industry Sectors
- Author Affiliations
- 1. Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
- 2. Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5, Canada
- 3. Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K.
- 4. Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
- 5. Department of Mathematics, University of California San Diego, La Jolla, CA, 92093-0112, U.S.A.
- 6. Department of Physics, Syracuse University, Syracuse, NY, 13244-1130, U.S.A.