Related papers: Discrete Dynamics: Gauge Invariance and Quantizati…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
The gauging of equations method, introduced in the preceding paper, is applied to the four-dimensional integral equations describing the strong interactions of three identical relativistic particles. In this way we obtain gauge invariant…
The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must…
When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD.…
Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…
We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom and it is represented by a quantum shifting superoperator that maps quantum…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by…
C. N. Yang's ideas about local gauge symmetry and non-integrable phases have been enormously fertile sources of inspiration in fundamental physics and in the quantum theory of matter. They also arise naturally in describing the dynamics of…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…