525 citations · 7.1k across the 109 of their papers we have counts for
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Renormalisation, wavelets and the Dirichlet-Shannon kernels
T. Thiemann
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation t…
Hamiltonian Renormalisation VII: Free fermions and doubler free kernels
T. Thiemann
The Hamiltonian renormalisation programme motivated by constructive QFT and Osterwalder-Schrader reconstruction which was recently launched for bosonic field theories is extended t…
Loop Quantum Gravity: An Inside View
Thomas Thiemann
This is a (relatively) non -- technical summary of the status of the quantum dynamics in Loop Quantum Gravity (LQG). We explain in detail the historical evolution of the subject an…
Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
T. Thiemann, O. Winkler
In this article we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator fo…
Gauge Field Theory Coherent States (GCS) : IV. Infinite Tensor Product and Thermodynamical Limit
T. Thiemann, O. Winkler
In the canonical approach to Lorentzian Quantum General Relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eigh…
Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
T. Thiemann, O. Winkler
In the preceding paper of this series of articles we established peakedness properties of a family of coherent states that were introduced by Hall for any compact gauge group and w…
Gauge Field Theory Coherent States (GCS) : I. General Properties
Thomas Thiemann
In this article we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states , labelled by a p…
Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
T. Thiemann
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued di…
Closed formula for Wilson loops for Quantum Yang-Mills Theory in two dimensions
Abhay Ashtekar, Jurek Lewandowski, Donald Marolf +2
A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups and and space-time topologies $\Rl^1…
The inverse loop transform
Thomas Thiemann
The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections modu…
An axiomatic approach to quantum gauge field theory
Thomas Thiemann
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the mod…
A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields
A. Ashtekar, J. Lewandowski, D. Marolf +2
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard…