Abstract
We consider interacting massive scalar quantum field theory in the future Rindler wedge. This is a model example of quantum field theory in curved space--time. On this simple example we show how dynamics of correlation functions depends on the choice of initial Cauchy surface, basis of modes and on the choice of initial state build with the use of the corresponding creation and annihilation operators. We show which choice of modes in the future Rindler wedge respects Poincare symmetry. But we do not restrict our attention only to these modes and the corresponding state.
Highlights
In the fundamental quantum field theory, one usually considers Poincareinvariant actions
We show how the dynamics of correlation functions depends on the choice of the initial Cauchy surface, the basis of modes, and the choice of the initial state built using the corresponding creation and annihilation operators
We show which choice of modes in the future Rindler wedge respects the Poincaresymmetry
Summary
In the fundamental quantum field theory, one usually considers Poincareinvariant actions Usually, this implies the consideration of such a Fock space ground state in which propagators are analytic functions of the geodesic distance between their points. To define uniquely correlation functions in this technique, one has to specify the initial state and there is no fundamental reason to restrict one’s attention only to the Poincareinvariant states, even if the action is generally covariant [3] or Poincareinvariant, as it is the case in Minkowski space-time. In this paper we propose considering the quantum field theory in the upper or future wedge of the entire Minkowski space-time and using the Rindler coordinates there. Appendix A presents a curious calculation of the In-Out transition amplitude in the free (gaussian) theory
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