Related papers: Weyl-gauge invariant proof of the Spin-Statistics …
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes…
The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrised model, Q, for the state vector evolution of spin 1/2 particles during measurement is developed. Q draws…
The aim of this paper is to establish a pseudo-differential Weyl calculus on graded nilpotent Lie groups $G$ which extends the celebrated Weyl calculus on $\mathbb{R}^n$. To reach this goal, we develop a symbolic calculus for a very general…
The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that…
A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J…
Since the 1935 proposal by Einstein Podolsky and Rosen the riddle of nonlocality, today demonstrated by innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
We present the world-line quantisation of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on ``phase space coordinates" $(x^\mu(\tau),p^\mu(\tau))$ which preserve the Minkowski metric and the…
Hamilton's action principle is formulated and extended in conformity with the gauge transformations underlying Weyl's geometry. The extended principle characterizes infinitely many equally likely trajectories with a particle traveling along…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one…
In the framework of vector model of spin, we discuss the problem of a covariant formalism \cite{Pomeranskii1998} concerning the discrepancy between relativistic and Pauli Hamiltonians. We show how the spin-induced non commutativity of a…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the…
Masanes, Galley and M\"uller [1] argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates together with an assumption they call the "possibility of state estimation". Their argument…
The Schur-Weyl states belong to a special class of states with a symmetry described by two Young and Weyl tableaux. Representation of physical systems in Hilbert space spanned on these states enables to extract quantum information hidden in…
We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding…
We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free of a physical wavefunction, is presented…
The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point…