Nonconventional functional calculus techniques in quantum field theories and in quantum gravity

Details Nonconventional functional calculus techniques in quantum field theories and in quantum gravity Nonconventional functional calculus techniques in quantum field theories and in quantum gravity

2007-10-11

arxiv.org/abs/0710.2337v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages

Scientific paper

In this exerpt we introduce the concept of the `nonconventional' calculus, outlining a prescription for making sense of the ultraviolet singularities which occur in quantum field theories with a view to addressing quantm gravity. We first show how these singularities arise when interpreting the canonical commutation relations for a general quantum field theory and then discuss a new intepretation which deals with them without using regularization procedures. We then discuss the relative commutativity of functional with spacetime variation and its implications for addressing the issue of time in quantum gravity in contrast to nongravitational field theories. We end with a brief introduction into how these concepts may be applied to the quantization of gravity in Ashtekar variables coupled to matter fields.

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