Related papers: An alternative to the gauge theoretic setting
General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
We propose a new point of view to gauge theories based on taking the action of symmetry transformations directly on the coordinates of space. Via this approach the gauge fields are not introduced at the first step, and they can be…
The gauge invariant minimal couplings for a class of relativistic free matter fields with global symmetry (related to usual charge conservation) have been obtained by incorporating an iterative Noether mechanism. Non-relativistic reduction…
In this lecture we discuss the basic ingredients for gauge invariant quantum field theories. We give an introduction to the elements of quantum field theory, to the construction of the basic Lagrangian for a general gauge theory, and…
We study the phase space structure of the Jackiw-Teitelboim model in its connection variables formulation where the gauge group of the field theory is given by local SL(2,R) (or SU(2) for the Euclidean model), i.e. the de Sitter group in…
Should nature be supersymmetric, then it will be described by Quantum Supergravity at least in some energy regimes. The currently most advanced description of Quantum Supergravity and beyond is Superstring Theory/M-Theory in 10/11…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
Within the premise of canonical quantisation, we re-examine the quantum structure of bosonic tensionless string theory. In the classical theory, the worldsheet metric degenerates and the Bondi-Metnzer-Sachs (BMS) algebra arises as the…
The classical theory of strain in material continua is reviewed and generalized to space-time. Strain is attributed to "external" (matter/energy fields) and intrinsic sources fixing the global symmetry of the universe (defects in the…
Starting from the observation that in Yang-Mills theory the Schroedinger state functional in the momentum representation is not gauge invariant, we investigate the reversed question: Which are the representations for the operators of a…
It is argued that the massive gauge field theory without the Higgs mechanism can well be set up on the gauge-invariance principle based on the viewpoint that a massive gauge field must be viewed as a constrained system and the Lorentz…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
This work presents instructive, yet comprehensive derivation of quantized gravity theories in relativistic, classical, and semi-classical spacetime structure based on the Poincar\'e, Galilean, and Bargmann algebra, respectively. The…
We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Future measurements of primordial non-Gaussianity can reveal cosmologically produced particles with masses of order the inflationary Hubble scale and their interactions with the inflaton, giving us crucial insights into the structure of…
We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime…