Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-04-11
J.Math.Phys. 45 (2004) 230
Physics
High Energy Physics
High Energy Physics - Theory
Title changed, further minor changes, references added, accepted for publication in J. Math. Phys
Scientific paper
It is shown that it is possible to define quantum field theory of a massless scalar free field on the Killing horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorphism invariance and turns out to be unitarily and algebraically equivalent to the analogous theory of a scalar field propagating inside Rindler spacetime, nomatter the value of the mass of the field in the bulk. More precisely, there exists a unitary transformation that realizes the bulk-boundary correspondence under an appropriate choice for Fock representation spaces. Secondly, the found correspondence is a subcase of an analogous algebraic correspondence described by injective *-homomorphisms of the abstract algebras of observables generated by abstract quantum free-field operators. These field operators are smeared with suitable test functions in the bulk and exact 1-forms on the horizon. In this sense the correspondence is independent from the chosen vacua. It is proven that, under that correspondence the ``hidden'' $SL(2,\bR)$ quantum symmetry found in a previous work gets a clear geometric meaning, it being associated with a group of diffeomorphisms of the horizon itself.
Moretti Valter
Pinamonti Nicola
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