Why is it interesting to consider quantum field theories where Lorentz symmetry is explicitly broken? The set of power-counting renormalizable theories is considerably"small Relaxing some assumptions can enlarge it, but often it enlarges it too much Without locality in principle every theory can be made finite Without unitarity even gravity can be renormalized Relaxing Lorentz invariance appears to be interesting in its own right could be useful to define the ultraviolet limit of quantum gravity and study extensions of the standard model Here we are interested in the renormalization of Lorentz violating theories obtained improving the behavior of propagators with the help of higher space derivatives and study under which conditions no higher time derivatives are turned on to be consistent with unitarity
The set of power-counting renormalizable theories is considerably “small” Relaxing some assumptions can enlarge it, but often it enlarges it too much Without locality in principle every theory can be made finite Without unitarity even gravity can be renormalized Relaxing Lorentz invariance appears to be interesting in its own right It could be useful to define the ultraviolet limit of quantum gravity and study extensions of the Standard Model Here we are interested in the renormalization of Lorentz violating theories obtained improving the behavior of propagators with the help of higher space derivatives and study under which conditions no higher time derivatives are turned on to be consistent with unitarity Why is it interesting to consider quantum field theories where Lorentz symmetry is explicitly broken?
Why is it interesting to consider quantum field theories where Lorentz symmetry is explicitly broken? The set of power-counting renormalizable theories is considerably"small Relaxing some assumptions can enlarge it, but often it enlarges it too much Without locality in principle every theory can be made finite Without unitarity even gravity can be renormalized Relaxing Lorentz invariance appears to be interesting in its own right could be useful to define the ultraviolet limit of quantum gravity and study extensions of the standard model Here we are interested in the renormalization of Lorentz violating theories obtained improving the behavior of propagators with the help of higher space derivatives and study under which conditions no higher time derivatives are turned on to be consistent with unitarity The approach that I formulate is based of a modified criterion of power counting dubbed weighted power counting
The set of power-counting renormalizable theories is considerably “small” Relaxing some assumptions can enlarge it, but often it enlarges it too much Without locality in principle every theory can be made finite Without unitarity even gravity can be renormalized Relaxing Lorentz invariance appears to be interesting in its own right It could be useful to define the ultraviolet limit of quantum gravity and study extensions of the Standard Model Here we are interested in the renormalization of Lorentz violating theories obtained improving the behavior of propagators with the help of higher space derivatives and study under which conditions no higher time derivatives are turned on to be consistent with unitarity The approach that I formulate is based of a modified criterion of power counting, dubbed weighted power counting Why is it interesting to consider quantum field theories where Lorentz symmetry is explicitly broken?
We may assume that there exists an energy range AL≤E≤ACPT that is well described by a Lorentz violating but CPT invariant quantum field theory If the neutrino mass has the Lorentz violating origin we propose, then AL N 10GeV and the mentioned range spans at least 4-5 orders of magnitude
We may assume that there exists an energy range that is well described by a Lorentz violating, but CPT invariant quantum field theory. and the mentioned range spans at least 4-5 orders of magnitude. If the neutrino mass has the Lorentz violating origin we propose, then
Scalar fields Break spacetime in two pieces MD=MD&MD d=d+d Break coordinates and momenta correspondingly: P=(p,P) Consider he=(0)2112 p)2 the free theory 2A This free theory is invariant under the "weighted scale transformation →ae →e-/a →qe where d=d+d/n is the" weighted dimension
Scalar fields Consider the free theory This free theory is invariant under the “weighted” scale transformation Break spacetime in two pieces: Break coordinates and momenta correspondingly: is the “weighted dimension
The prop or k2+ k_) behaves better than usual in the barred directions Adding"Weighted relevant terms we get a free theory 入2(1-k/n) (2)2+ that flows to the previous one in the Uv and to the lorentz invariant free theory in the infrared (actually, the IR Lorentz recovery is much more subtle, see below)
The propagator behaves better than usual in the barred directions Adding “weighted relevant’’ terms we get a free theory that flows to the previous one in the UV and to the Lorentz invariant free theory in the infrared (actually, the IR Lorentz recovery is much more subtle, see below)