Related papers: Group theoretical formulation of free fall and pro…
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order…
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
We investigate the group field theory formulation of the EPRL/FK spin foam models. These models aim at a dynamical, i.e. non-topological formulation of 4D quantum gravity. We introduce a saddle point method for general group field theory…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…
In this short note, we study the variation of orbital integrals, as traces on the group algebra $G$, under the deformation groupoid. We show that orbital integrals are continuous under the deformation. And we prove that the pairing between…
Current quantisations of fermions in cylindrical coordinates are shown to be inadequate in calculating some single-particle expectation values. This paper develops an alternate quantisation, applicable to one-particle states, which is…
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
We show in general that for a relativistic theory with curved momentum space, i.e.~a theory with deformed relativistic symmetries, the physical velocity of particles coincides with their group velocity. This clarifies a long-standing…
The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion…
We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbors depending on the sign of their relative velocity.…
To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the…
We prove the decidability of the elementary theory of a free group.
We study the spatial dependence of the quantum friction effect for an atom moving at a constant velocity, in a parallel direction to a material plane. In particular, we determine the probability per unit time and unit area, for exciting…
We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These…
We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach.…