相关论文: The Quantum Geometry of Spin and Statistics

The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…

We use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quantum systems by means of a set of equations resembling the…

Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…

The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…

We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong…

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes…

Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments…

Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…

The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…

Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…

We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…

We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum…

The analogy between the Skyrme and Higgs field leads to the conjecture that all fermions are skyrmions and thus always carry conserved quantum numbers, which are identified with baryon or lepton quantum numbers. This connection between spin…

In multiparticle quantum interference, bosons show rather generally the tendency to bunch together, while fermions can not. This behavior, which is rooted in the different statistics of the particles, results in a higher coincidence rate…

The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…

We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…

In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…