A ground state for the causal diamond in 2 dimensions

Afshordi, Niayesh; Buck, Michel; Dowker, Fay; Rideout, David; Sorkin, Rafael D.; Yazdi, Yasaman K.

doi:10.1007/jhep10(2012)088

Cited by 34 publications

(118 citation statements)

References 31 publications

Supporting

Mentioning

105

Contrasting

Order By: Relevance

“…A more careful approach was adopted in [3] where the massless SJ vacuum was calculated explicitly in a 2D causal diamond D of length 2L. Evaluating W SJ in the center of the diamond, i.e., with | x − x | << L and | x|, | x | << L it was shown that |0 SJ ∼ |0 mink .…”

Section: The Sj Prescriptionmentioning

confidence: 99%

“…We evaluate the above series by using the method developed in [13] and used in [3,4], details of which can be found in Appendix B. This leads to…”

Section: Completeness Of the Eigenfunctionsmentioning

confidence: 99%

“…The associated SJ Wightman function W SJ (or two point function) is then simply the positive part of i∆. W SJ can be shown to be the unique vacuum which satisfies the following conditions [1,3] W (X, X ) − W (X , X) = i∆(X, X ) Commutator condition W (X, X ) − W * (X , X) = 0 Hermiticity…”

Section: Introductionmentioning

confidence: 99%

“…As a result there are very few cases in which W SJ has been obtained explicitly. These include the massless free scalar SJ vacuum in a 2D flat causal diamond [3,4], a patch of trousers spacetime [5] and the ultrastatic slab spacetime [6]. In this work, we study the SJ vacuum for a massive free scalar field in the 2D flat causal diamond D of length 2L, both in the continuum and on a causal set C D obtained from sprinkling into D.…”

Section: Introductionmentioning

confidence: 99%

“…As in [3] we consider two regimes of interest: one in the center of the diamond, and the other at the corner. In a small central region D l of size l, we find analytically that W SJ resembles the massless Minkowski vacuum W mink 0 up to a small mass-dependent constant center m , rather than the massive Minkowski vacuum W mink m .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond

Mathur

Surya

2019

Phys. Rev. D

View full text Add to dashboard Cite

We study the massive scalar field Sorkin-Johnston (SJ) Wightman function WSJ restricted to a flat 2D causal diamond D of linear dimension L. Our approach is two-pronged. In the first, we solve the central SJ eigenvalue problem explicitly in the small mass regime, up to order (mL) 4 . This allows us to formally construct WSJ up to this order. Using a combination of analytical and numerical methods, we obtain expressions for WSJ both in the center and the corner of D, to leading order. We find that in the center, WSJ is more like the massless Minkowski Wightman function W mink 0 than the massive one W mink m , while in the corner it corresponds to that of the massive mirror W mirror m . In the second part, in order to explore larger masses, we perform numerical simulations using a causal set approximated by a flat 2D causal diamond. We find that in the center of the diamond the causal set SJ Wightman function W c SJ resembles W mink 0 for small masses, as in the continuum, but beyond a critical value mc it resembles W mink m , as expected. Our calculations suggest that unlike W mink m , WSJ has a well-defined massless limit, which mimics the behavior of the Pauli Jordan function underlying the SJ construction. In the corner of the diamond, moreover, W c SJ agrees with W mirror m for all masses, and not, as might be expected, with the Rindler vacuum. * abhishekmathur@rri.res.in arXiv:1906.07952v2 [hep-th]

show abstract

Section: The Sj Prescriptionmentioning

confidence: 99%

“…We evaluate the above series by using the method developed in [13] and used in [3,4], details of which can be found in Appendix B. This leads to…”

Section: Completeness Of the Eigenfunctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%