Abstract
We propose a new discretization scheme for field theory, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Working in a discrete representation of that algebra, one obtains naturally a discretization scheme. The original theory should be recovered for representations of large dimensionality. The procedure is illustrated with space-like coordinates that form a Heisenberg algebra. Advantages exist with respect to conventional lattice field theory: fermions can easily be put on a lattice and the continuum limit is recovered without the problems appearing in the conventional formalism; however other types of problems appear.
Keywords
- Continuum Limit
- Discretization Scheme
- Radial Symmetry
- Discrete Representation
- Heisenberg Algebra
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Acatrinei, C.S. (2012). A New Discretization Scheme in Field Theory. In: Adam, G., Buša, J., Hnatič, M. (eds) Mathematical Modeling and Computational Science. MMCP 2011. Lecture Notes in Computer Science, vol 7125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28212-6_10
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DOI: https://doi.org/10.1007/978-3-642-28212-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28211-9
Online ISBN: 978-3-642-28212-6
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