Related papers: Weyl-gauge invariant proof of the Spin-Statistics …

The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…

These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a…

We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincar\'e invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations,…

We explore the experimental predictions of the local scale invariant, non-Hermitian pilot-wave (de Broglie-Bohm) formulation of quantum theory introduced in arXiv:2601.03567. We use Weyl's definition of gravitational radius of charge to…

It has been known for some time that topological geons in quantum gravity may lead to a complete violation of the canonical spin-statistics relation : there may exist no connection between spin and statistics for a pair of geons. We present…

We reply to the critique by Pucchini and Vucetich of our construction of a non-relativistic proof of the spin-statistics connection using SU(2) invariance and a Weiss-Schwinger action principle.

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically…

The existence of a possible connection between spin and statistics is explored within the framework of Galilean covariant field theory. To this end fields of arbitrary spin are constructed and admissible interaction terms introduced. By…

We discuss the generalization of the local renormalization group approach to theories in which Weyl symmetry is gauged. These theories naturally correspond to scale invariant - rather than conformal invariant - models in the flat space…

I suggest that the Spin-Statistics connection is a consequence of the phase shifts on quantum scattering amplitudes due to the induced gravitomagnetic field of the whole Universe at critical density. This connection was recently brought out…

In a previous paper [quant-ph/0207017] I gave an elementary proof, starting from stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles must be bosons. Since then it has been suggested that my proof…

The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are…

We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…

In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a…

We show how to lift a generic non-scale invariant action in Einstein frame into a locally conformally-invariant (or Weyl-invariant) theory and present a new general form for Lagrangians consistent with Weyl symmetry. Advantages of such a…

We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories,…

We propose that the gauge principle of d-dimensional Euclidean quantum gravity is Weyl invariance in its stochastic (d+1)-dimensional bulk. Observables are defined as depending only on conformal classes of d-dimensional metrics. We work…

A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is…

Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…

We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…