Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-10-08
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
61 pages; a version with better graphics and some related materials can be obtained at http://math.ucr.edu/~derek/pform
Scientific paper
Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a `chain field theory' -- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds. This, in particular, gives a notion of time evolution from one `spacelike slice' of discrete spacetime to another.
No associations
LandOfFree
Lattice p-Form Electromagnetism and Chain Field Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lattice p-Form Electromagnetism and Chain Field Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lattice p-Form Electromagnetism and Chain Field Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-192719