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In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical value of zero-point energy suggested by quantum field theory.
Loop quantum cosmology (LQC) is a symmetry-reduced model of classical general relativity quantized using methods that mimic those of loop quantum gravity (LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches.
The operator constituting each equation, (−γ μ P μ + mc) = (−iħγ μ ∂ μ + mc), is a 4 × 4 matrix, because of the γ μ matrices, and the mc term scalar-multiplies the 4 × 4 identity matrix (usually not written for simplicity). Explicitly, in the Dirac representation of the gamma matrices: [1]
To give some context for the general reader, the naive expectation for asymptotically flat spacetime symmetries, i.e., symmetries of spacetime seen by observers located far away from all sources of the gravitational field, would be to extend and reproduce the symmetries of flat spacetime of special relativity, viz., the Poincaré group, also called the inhomogeneous Lorentz group, [2] which is ...
The third term is known as the color anomaly, a consequence of the Peccei–Quinn symmetry being anomalous, with determined by the choice of PQ charges for the quarks. If the symmetry is also anomalous in the electromagnetic sector, there will additionally be an anomaly term coupling the axion to photons.
The basic idea is simply that the vacuum expectation values of Wilson loops in Chern–Simons theory are link invariants because of the diffeomorphism-invariance of the theory. To calculate these expectation values, however, Witten needed to use the relation between Chern–Simons theory and a conformal field theory known as the Wess–Zumino ...
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