Uploaded on
It is shown that UV-finite Lorentz covariant and gauge invariant quantum field theories can be constructed based on the premise that Lorentzian spacetime is emergent from a statistically averaged …
We have emailed the verification/download link to "".
Login to your email and click the link to download the file directly.
Check your bulk/spam folders if you can't find our mail.
It is shown that UV-finite Lorentz covariant and gauge invariant quantum field theories can be constructed based on the premise that Lorentzian spacetime is emergent from a statistically averaged …
It is shown that UV-finite Lorentz covariant and gauge invariant quantum field theories can be constructed based on the premise that Lorentzian spacetime is emergent from a statistically averaged ensemble of discrete “pre-spacetimes” having Euclidean signature via a local Wick rotation. A continuum approximation to the underlying discrete theory is developed by expanding fields in terms of a finite number of eigenfunctions of an appropriate gauge covariant Laplacian. The resulting Euclidean spacetime theory is gauge invariant and rotation covariant. It is shown that Wick rotation is uniquely defined locally with respect to a frame at rest relative to a background gravitational field such that rotation covariant results in Euclidean spacetime are mapped to Lorentz covariant results upon Wick rotation. Starting from Hamiltonian formulations, partition functions are derived for Yang-Mills theory and for quantum gravity that contain a finite number of field integrations. A perturbative expansion for the eigenfunctions is developed and it is shown that there are no UV divergences in the theory since there is only a finite number of degrees of freedom. For the case of Yang-Mills theory, quantities that are divergent in the standard approach are replaced with finite quantities that depend on the length scale, L_d, of the discrete pre-spacetimes. In the case of quantum gravity, it is shown that a perturbation expansion in powers of the ratio of the Planck length to L_d can be carried out if it is assumed that this is a small quantity. As concrete examples of the formalism, vacuum polarization and electron self-energy at one loop order in QED are calculated and standard results are obtained with a finite physical cutoff of 2 pi / L_d.
Views
Actions
Embeds 0
Report content