Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background

Details Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background

Sep 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvd..34.1768w&link_type=abstract

Physical Review D (Particles and Fields), Volume 34, Issue 6, 15 September 1986, pp.1768-1775

Physics

10

Theory Of Quantized Fields, Lagrangian And Hamiltonian Approach

Scientific paper

It is shown that by performing an appropriate time-dependent canonical transformation on the action for a scalar field theory in a Robertson-Walker background one can obtain a Hamiltonian whose ground state ||vt0> at any initial time t0 has several desirable properties. First of all its field anticommutator expectation values G(x,y) =@BB are of the Hadamard form: G(x,y)-->x-->y(1/4π2)[1/σ +1/2[M2+(ξ-(1/6))R]ln (σ)+O(σ0)], where √2σ is the geodesic distance between x and y, for all values of t0. Second, the divergent part of the energy density is independent of t0, thus allowing a state-independent renormalization of the energy density. If the appropriate canonical transformation is not performed, the aforementioned results fail to hold.

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