Related papers: Weyl-gauge invariant proof of the Spin-Statistics …
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network;…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…
A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the…
Pure $R^2$ gravity was considered originally to possess only global scale symmetry. It was later shown to have the larger restricted Weyl symmetry where it is invariant under the Weyl transformation $g_{\mu\nu} \to \Omega^2(x)\, g_{\mu\nu}$…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
The twist-deformation of the Poincar\'e algebra as symmetry of the field theories on noncommutative space-time with Heisenberg-like commutation relation is discussed in connection to the relation between a sound approach to the twist and…
Interactions of gauge-invariant systems are severely constrained by several consistency requirements. One is the preservation of the number of gauge symmetries, another is causal propagation. For lower-spin fields, the emphasis is usually…
Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely…
Recently, a topological proof of the spin-statistics Theorem has been proposed for a system of point particles which does not require relativity or field theory, but assumes the existence of antiparticles. We extend this proof to a system…
We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance…
Bialek, Callan and Strong have recently given a solution of the problem of determining a continuous probability distribution from a finite set of experimental measurements by formulating it as a one-dimensional quantum field theory. This…
In this paper we discuss on the phenomenological viability of nonmetricity theories of gravity which are based in the class of generalized Weyl spacetimes -- denoted by $W_4$ -- where arbitrary nonmetricity is allowed. This class of…
The group theoretical approach to the relativistic wave equations on the real reducible spaces for spin~0, 1/2 and~1 massless particles is considered. The invariant wave equations which determine the appropriate irreducible representations…
It is shown in the present paper that the transformation relating a parallel transported vector in a Weyl space to the original one is the product of a multiplicative gauge transformation and a proper orthochronous Lorentz transformation.…
Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction…
We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same…