Abstract
We study a complex free scalar field theory on a noncommutative background spacetime called $\kappa$-Minkowski. In particular we address the problem of second quantization. We obtain the algebra of creation and annihilation operators in an explicitly covariant way. Our procedure does not use canonical/Hamiltonian formulations, which turn out to be ill-defined in our context. Instead we work in a spacetime covariant way by introducing a noncommutative Pauli-Jordan function. This function is obtained as a generalization of the ordinary, commutative, one by taking into account the constraints imposed by the symmetries of our noncommutative spacetime. The Pauli-Jordan function is later employed to study the structure of the light cone in $\kappa$-Minkowski spacetime, and to draw conclusions on the superluminal propagation of signals.
Highlights
Quantum field theory (QFT) on Minkowski spacetime is arguably the most successful paradigm in physics, both for the precision with which some of its predictions have been tested, and for the variety of phenomena it is capable to describe
II we briefly review the mathematical tools needed for our analysis, and give a brief recap of the things we already know about scalar fields and the geometry of momentum space
At the time, the understanding of κ-Minkowski’s momentum space was somewhat limited, and this led the authors of [11,13] to define their Green functions as contour integrals on the complexification of a particular timelike “energy” coordinate on momentum space. Complexifying this coordinate breaks diffeomorphism invariance and introduces an infinite tower of poles of the Green functions. The authors interpreted this as a physical feature of the theory
Summary
Quantum field theory (QFT) on Minkowski spacetime is arguably the most successful paradigm in physics, both for the precision with which some of its predictions have been tested, and for the variety of phenomena it is capable to describe. The Planck scale (or rather its inverse, which in ħ 1⁄4 c 1⁄4 1 units is the Planck length Lp ∼ 10−35 m) plays the role of noncommutativity parameter, similar to that played by ħ in ordinary quantum mechanics In particular it appears on the right-hand side of uncertainty relations between coordinate functions xμ , and there is a sense in which the noncommutative geometry described by this algebra should look like the commutative geometry of Minkowski spacetime in the large-scale/infrared limit. Because of our lack of understanding of 3 þ 1D quantum gravity, we presently have no way to repeat the exercise done in 2 þ 1D of integrating away the gravitational field to uncover the correct effective theory of matter on a quantum-gravity background For this reason, we are compelled to study all the possible 3 þ 1D noncommutative geometries whose noncommutativity parameter depends on the Planck length.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
