A ground state for the causal diamond in 2 dimensions
 Niayesh Afshordi,
 Michel Buck,
 Fay Dowker,
 David Rideout,
 Rafael D. Sorkin,
 Yasaman K. Yazdi
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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 twodimensional 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.
 S. Fulling, Aspects of quantum field theory in curved spacetime, London Mathematical Society Student Texts volume 17, London U.K. (1989).
 R.M. Wald, The formulation of quantum field theory in curved spacetime, arXiv:0907.0416 [INSPIRE].
 R.D. Sorkin, Scalar field theory on a causal set in histories form, J. Phys. Conf. Ser. 306 (2011)012017 [arXiv:1107.0698] [INSPIRE]. CrossRef
 N. Afshordi, S. Aslanbeigi and R.D. Sorkin, A distinguished vacuum state for a quantum field in a curved spacetime: formalism, features and cosmology, JHEP 08 (2012) 137 [arXiv:1205.1296] [INSPIRE]. CrossRef
 S. Johnston, Feynman propagator for a free scalar field on a causal set, Phys. Rev. Lett. 103 (2009)180401 [arXiv:0909.0944] [INSPIRE]. CrossRef
 S.P. Johnston, Quantum fields on causal sets, arXiv:1010.5514 [INSPIRE].
 C.J. Fewster and R. Verch, On a recent construction of ’vacuumlike’ quantum field states in curved spacetime, Class. Quant. Grav. 29 (2012) 205017 [arXiv:1206.1562] [INSPIRE]. CrossRef
 S.R. Coleman, There are no Goldstone bosons in two dimensions, Commun. Math. Phys. 31 (1973)259 . CrossRef
 E. Abdalla, M. Abdalla and K. Rothe, Nonperturbative methods in 2 dimensional quantum field theory, World Scientific, Singapore (1991). CrossRef
 M. Faber and A. Ivanov, On the ground state of a free massless (pseudo)scalar field in twodimensions, hepth/0212226 [INSPIRE].
 W. Rindler, Kruskal space and the uniformly accelerated frame, Amer. J. Phys. 34 (1966) 1174. CrossRef
 W. Rindler, Relativity: special, general, and cosmological, Oxford University Press, Oxofrd U.K. (2006).
 S.A. Fulling, Nonuniqueness of canonical field quantization in Riemannian spacetime, Phys. Rev. D 7 (1973) 2850 [INSPIRE].
 P. Davies, Scalar particle production in Schwarzschild and Rindler metrics, J. Phys. A 8 (1975)609 .
 W. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
 N. Bogoliubov, D. Shirkov, and E. Henley, Introduction to the theory of quantized fields, Physics Today 13 (1960) 40. CrossRef
 M. Stone, Linear transformations in Hilbert space and their applications to analysis, American Mathematical Society, U.S.A. (1979).
 M. Speigel, The summation of series involving roots of transcendental equations and related applications, J. Appl. Phys. 24 (1953) 1103 . CrossRef
 N. Birrell and P. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1984).
 P. Davies and S. Fulling, Radiation from a moving mirror in twodimensional spacetime conformal anomaly, Proc. Roy. Soc. Lond. A 348 (1976) 393 [INSPIRE].
 L. Bombelli, J. Lee, D. Meyer and R. Sorkin, Spacetime as a causal set, Phys. Rev. Lett. 59 (1987)521 [INSPIRE]. CrossRef
 R.D. Sorkin, Causal sets: Discrete gravity, in Lectures on quantum gravity, proceedings of the Valdivia Summer School, Valdivia, Chile, January 2002, A. Gomberoff and D. Marolf eds., Plenum, U.S.A. (2005), grqc/0309009 [INSPIRE].
 J. Henson, The causal set approach to quantum gravity, in Approaches to quantum gravity: towards a new understanding of space and time, D. Oriti ed., Cambridge University Press, Cambridge U.K. (2006), grqc/0601121 [INSPIRE].
 L. Bombelli, J. Henson and R.D. Sorkin, Discreteness without symmetry breaking: a theorem, Mod. Phys. Lett. A 24 (2009) 2579 [grqc/0605006] [INSPIRE].
 R.D. Sorkin, Does locality fail at intermediate lengthscales, in Approaches to quantum gravity: towards a new understanding of space and time, D. Oriti ed., Cambridge University Press, Cambridge U.K. (2006), grqc/0703099 [INSPIRE].
 S. Johnston, Particle propagators on discrete spacetime, Class. Quant. Grav. 25 (2008) 202001 [arXiv:0806.3083] [INSPIRE]. CrossRef
 P. Dirac, The lagrangian in quantum mechanics, Phys. Zeit. Sooviet Un. 3 (1933) 64.
 Title
 A ground state for the causal diamond in 2 dimensions
 Journal

Journal of High Energy Physics
2012:88
 Online Date
 October 2012
 DOI
 10.1007/JHEP10(2012)088
 Online ISSN
 10298479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Field Theories in Lower Dimensions
 Nonperturbative Effects
 Lattice Quantum Field Theory
 Stochastic Processes
 Industry Sectors
 Authors

 Niayesh Afshordi ^{(1)} ^{(2)}
 Michel Buck ^{(3)}
 Fay Dowker ^{(2)} ^{(3)} ^{(4)}
 David Rideout ^{(5)}
 Rafael D. Sorkin ^{(2)} ^{(6)}
 Yasaman K. Yazdi ^{(1)}
 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, 920930112, U.S.A.
 6. Department of Physics, Syracuse University, Syracuse, NY, 132441130, U.S.A.