Polarized vector bosons on the de Sitter expanding universe

Abstract

The quantum theory of the vector field minimally coupled to the gravity of the de Sitter spacetime is built in a canonical manner starting with a new complete set of quantum modes of given momentum and helicity derived in the moving chart of conformal time. It is shown that the canonical quantization leads to new vector propagators which satisfy similar equations as the propagators derived by Tsamis and Woodard [{\em J.Math.Phys.} {\bf 48} (2007) 052306] but having a different structure. The one-particle operators are also written down pointing out that their properties are similar with those found already in the quantum theory of the scalar, Dirac and Maxwell free fields.Comment: 17 pages no figure

The Quantum Theory of the Free Maxwell Field on the de Sitter Expanding Universe

“…Moreover, we pointed out that the momentum and energy bases yield the same vacuum state which is analogous to the Bunch-Davies vacuum of the scalar field [14]. In this framework we obtained new Dirac [7] and Proca [13] propagators but by recovering the well-known one of the scalar field [15]. However, the principal virtue of our approach is the opportunity of calculating the conserved one-particle operators corresponding to the Killing vectors of the dS geometry now in both the momentum and energy bases.…”

“…So we obtained the energy bases of these fields which are equivalent to the corresponding momentum ones through unitary transformations. Both these types of bases have suitable orthogonality and completeness properties allowing us to perform the canonical quantization of the scalar [11], Dirac [7] and (massive) Proca [13] free fields on dS manifolds. Moreover, we pointed out that the momentum and energy bases yield the same vacuum state which is analogous to the Bunch-Davies vacuum of the scalar field [14].…”

The physical meaning of the de Sitter invariants

“…Recently we presented the complete quantum theory of the Proca field in the de Sitter moving chart with conformal time [21]. However, here we must consider the vector field in non-holonomic frames where we can exploit the results of the previous section.…”

“…Hereby we selected various sets of commuting operators determining the quantum modes of the scalar [20], vector [21,22] and Dirac [23][24][25] fields.…”

Reply to “Comment on ‘Fermion production in a magnetic field in a de Sitter universe”’

“…The perturbative QED on the de Sitter spacetime was constructed in [14] where it is shown that that a mandatory condition for quantifying the whole theory is to choose and fix the Coulomb gauge. Moreover, this seems to be a specific feature of the de Sitter geometry as long as the massless limit of the free Proca field on this background [17], gives just the free Maxwell field in Coulomb gauge.…”