Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories Export

@article{citeulike:5695366, abstract = {It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that at least part of this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points, are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized. Of course, to show that the entire theory is finite requires more: one would need to know what the physical observables are, apart from the Hamiltonian constraint, and whether they are also finite. However, with the results given in this paper this question can now be answered, at least in principle.}, author = {Thiemann, T.}, citeulike-article-id = {5695366}, citeulike-linkout-0 = {http://dx.doi.org/10.1088/0264-9381/15/5/012}, doi = {10.1088/0264-9381/15/5/012}, journal = {Classical and Quantum Gravity}, keywords = {constraint, divergences, hamiltonian, qft, quantum-gravity, regularization, spin-networks, uv}, number = {5}, pages = {1281--1314}, posted-at = {2009-09-01 03:43:38}, priority = {2}, title = {Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories}, url = {http://dx.doi.org/10.1088/0264-9381/15/5/012}, volume = {15}, year = {1998} }

TY - JOUR ID - citeulike:5695366 L3 - citeulike-article-id:5695366 N2 - It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that at least part of this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points, are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized. Of course, to show that the entire theory is finite requires more: one would need to know what the physical observables are, apart from the Hamiltonian constraint, and whether they are also finite. However, with the results given in this paper this question can now be answered, at least in principle. IS - 5 JF - Classical and Quantum Gravity EP - 1314 TI - Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories VL - 15 SP - 1281 KW - constraint KW - divergences KW - hamiltonian KW - qft KW - quantum-gravity KW - regularization KW - spin-networks KW - uv AU - Thiemann, T PY - 1998/// UR - http://dx.doi.org/10.1088/0264-9381/15/5/012 ER -