Related papers: Discerning Elementary Particles
In a series of recent papers, Simon Saunders, Fred Muller and Michael Seevinck have collectively argued, against the philosophy of quantum mechanics folklore, that some non-trivial version of Leibniz's principle of the identity of…
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with…
As argued in our previous papers, it would be more natural to modify the standard approach to quantum theory by requiring that i) one unitary irreducible representation (UIR) of the symmetry algebra should describe a particle and its…
Bohr's dictum "Physical phenomena are observed relative to different experimental setups" is applied to a set of binary elements that represent the smallest units of information. A description relative to "macroscopic" setups of such…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
We examine a recent argument that ``identical'' quantum particles with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black's spheres,…
Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded…
According to classical physics particles are basic building blocks of the world. Classical particles are distinguishable objects, individuated by physical characteristics. By contrast, in quantum mechanics the standard view is that…
Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This…
A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via…
The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this.…
We introduce the key ideas and mathematical tools central to modern discussions of collapse. We assume knowledge of basic quantum mechanics -- the Schr\"{o}dinger evolution of states in Hilbert space, the Born probability rule, the Dirac…
We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…
We reconsider the (non-relativistic) quantum theory of indistinguishable particles on the basis of Rieffel's notion of C*-algebraic (`strict') deformation quantization. Using this formalism, we relate the operator approach of Messiah and…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
We study the Heisenberg quantization for the systems of identical particles in noncommtative spaces. We get fermions and bosons as a special cases of our argument, in the same way as commutative case and therefore we conclude that the Pauli…
In standard Poincare and anti de Sitter SO(2,3) invariant theories, antiparticles are related to negative energy solutions of covariant equations while independent positive energy unitary irreducible representations (UIRs) of the symmetry…
In computational physics it is standard to approximate continuum systems with discretised representations. Here we consider a specific discretisation of the continuum complex Hilbert space of quantum mechanics - a discretisation where…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…