arXiv subjects

Michael J. York

Publications and source records attributed to Michael J. York.

4 recordsLinked to original sources

arXiv2000

Symmetrizing The Symmetrization Postulate

Reasonable requirements of (a) physical invariance under particle permutation and (b) physical completeness of state descriptions, enable us to deduce a Symmetric Permutation Rule(SPR): that by taking care with our state descriptions, it is always possible to construct state vectors (or wave functions) that are purely symmetric under pure permutation for all particles, regardless of type distinguishability or spin. The conventional exchange antisymmetry for two identical half-integer spin particles is shown to be due to a subtle interdependence in the individual state descriptions arising from an inherent geometrical asymmetry. For three or more such particles, however, antisymmetrization of the state vector for all pairs simultaneously is shown to be impossible and the SPR makes observably different predictions, although the usual pairwise exclusion rules are maintained. The usual caveat of fermion antisymmetrization - that composite integer spin particles (with fermionic consitituents) behave only approximately like bosons - is no longer necessary.

quant-ph↗

arXiv1999

Permutation Symmetry For Many Particles

We consider the implications of the Revised Symmetrization Postulate (see quant-ph/9908078) for states of more than two particles. We show how to create permutation symmetric state vectors and how to derive alternative state vectors that may be asymmetric for any pair by creating asymmetric interdependencies in their state descriptions. Because we can choose any pair to create such an asymmetry, the usual generalized exclusion rules which result, apply simultaneously to any pair. However, we distinguish between simultaneous pairwise exclusion rules and the simultaneous pairwise anti-symmetry of the conventional symmetrization postulate. We show how to construct a variety of state vectors with multiple interdependencies in their state descriptions and various exchange asymmetries - including one which is anti-symmetric under exchange of two bosons - all without violating the spin-statistics theorem. We conjecture that it is possible to construct state vectors for arbitrary mixes of bosons and fermions that emulate the conventional symmetrization postulate in a limited way and give examples. We also prove that it is not possible to define a single state vector that simultaneously obeys the conventional symmetrization postulate in its standard form (in which the exchange phase does not depend on the spins of additional particles that are present) for every pair that can be interchanged.

quant-ph↗

arXiv1999

Identity, Geometry, Permutation And The Spin-Statistics Theorem

We examine historic formulations of the spin-statistics theorem from a point of view that distinguishes between the observable consequences and the ``symmetrization postulate''. In particular, we make a critical analysis of concepts of particle identity, state distinguishability and permutation, and particle ``labels''. We discuss how to construct unique state vectors and the nature of the full state descriptions required for this -- in particular the elimination of arbitrary $2π$ rotations on fermion spin quantization frames and argue that the failure to do this renders the conventional symmetrization postulate (and previous ``proofs'' of it) at best {\em incomplete}. We discuss particle permutation in a general way for any pairs of particles, whether identical or not, and make an essential distinction between exchange and pure permutation. We prove a revised symmetrization postulate that allows us to construct state vectors that are naturally symmetric under pure permutation, {\em for any spin}. The significance of particle labels (which, in the exchange operation, are not permuted along with other variables) is then that they stand in for any asymmetry (order dependence) that is present in the full state descriptions necessary for unique state vectors but not explicit in the regular state variables. {\em The exchange operation is then the physical transformation that reverses any asymmetry implicit in the labels}. We point out a previously unremarked geometrical asymmetry between all pairs of particles that is present whenever we choose a common frame of reference. We compute the exchange phase for various state vectors using different spin quantization frames, and prove the Pauli Exclusion Principle and its generalization to arbitrary spin.

quant-ph↗

arXiv1998

Spatial Asymmetry For Particle Pairs And The Spin-Statistics Theorem

We discuss the conditions under which identical particles may yet be distinguishable and the relationship between particle permutation and exchange. We show that we can always define permutation-symmetric state vectors. When the particles are completely indistinguishable, then exchange is equivalent to permutation and therefore the exchange eigenvalue for such permutation-symmetric state vectors is always +1. Exchange asymmetry arises when the particles are physically distinguishable, even though otherwise identical, and can be computed from the transformations that arise when the distinguishing features are reversed. There is a fundamental spatial asymmetry between the relative orientations of any two vectors in a common frame of reference that persists even in the limit that the vectors coincide. For a pair of particles this asymmetry between their spin quantization frames renders them distinguishable even when otherwise identical. In the conventional construction, this distinction is not properly accounted for. Particle exchange is then equivalent to reversing this relative orientation --- which requires a relative rotation by 2pi on the spin quantization frame of one particle with respect to the other, thus resulting in the conventional exchange phase.

quant-ph↗