C. R. Hagen
The existence of a possible connection between spin and statistics is explored within the framework of Galilean covariant field theory. To this end fields of arbitrary spin are constructed and admissible interaction terms introduced. By explicitly solving such a model in the two particle sector it is shown that no spin and statistics connection can be established.
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We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we characterize translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined in Nimmrichter and Hornbergerl. [Phys. Rev. Lett. 110, 16 (2013)].
The second central extension of the planar Galilei group has been alleged to have its origin in the spin variable. This idea is explored here by considering local Galilean covariant field theory for free fields of arbitrary spin. It is shown that such systems generally display only a trivial realization of the second central extension. While it is possible to realize any desired value of the extension parameter by suitable redefinition of the boost operator, such an approach has no necessary connection to the spin of the basic underlying field.
We replay to the critique by Sudarshan and Shaji of our argument of impossibility to obtain a non-relativistic proof of the spin-statistics theorem in the Galilean frame.
We reply to the critique by Pucchini and Vucetich of our construction of a non-relativistic proof of the spin-statistics connection using SU(2) invariance and a Weiss-Schwinger action principle.
Here we explore the possibility to obtain a non-relativistic proof of the spin-statistics theorem. First, we examine the structure of axioms and theorems involved in a relativistic Schwinger-like proof of the spin-statistics relation. Second, starting from this structure we identify the relativistic assumptions. Last, we reformulate these assumptions in order to obtain a Galilean proof. We conclude that the spin-statistics theorem cannot be deduced into the framework of Galilean quantum field theories for three space dimensions because two of the assumptions needed to prove the theorem are inc…
Galilean One-Particle Kinematics from a Smooth Family of Reference States
本文通过平滑参考态家族构建伽利略单粒子动力学，利用可观测量-生成量对应关系和局部惯性组合，得出不可约表示的等价性及自旋覆盖作用与中心提升-平移扭量。
Cartan's spacetime reformulation of the Newtonian theory of gravity is a generally-covariant Galilean-relativistic limit-form of Einstein's theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the degenerate `metric' structure of spacetime remains fixed with two mutually orthogonal non-dynamical metrics, one spatial and the other temporal. The spacetime according to this theory is, nevertheless, curved, duly respecting the principle of equivalence, and the non-metric gravitational connection-fie…
The Galilean symmetry and the Poincare symmetry are usually taken as the fundamental (relativity) symmetries for `nonrelativistic' and `relativistic' physics, respectively, quantum or classical. Our fully group theoretical formulation approach to the theories, together with its natural companion of mechanics from symplectic geometry, ask for different perspectives. We present a sketch of the full picture here, emphasizing aspects which are different from the more familiar picture. The letter summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or co…
We derive an equivalent traveling wave form description for Dirac field. In the non-relativistic limit, such form can reduce to inverse-Galilean transformed Schrodinger-type equation. We find that, the resulting two-component Schrodinger-type equation from the reduction of traveling wave form description of Dirac field is different to the naive Galilean transformed Schrodinger equation. Taking into account the interactions of the system to electromagnetic field by adding proper forms of covariant derivative, the traveling wave form description for Pauli equation can be similarly obtained in th…
We explore the possibility that the connection between spin and statistics in quantum physics is of dynamical origin. We suggest that the gravitational field could provide a fully local mechanism for the phase that arises when fermionic and bosonic particles are exchanged. Our results hold even if the symmetry of space and time is Galilean, thus establishing that special relativity is not needed to explain the existence of spin (although it does motivate the introduction of creation and annihilation of particles, but this is a separate issue). We provide a model for the coupling between a part…
Translation-covariant Markovian master equations used in the description of decoherence and dissipation are considered in the general framework of Holevo's results on the characterization of generators of covariant quantum dynamical semigroups. A general connection between the characteristic function of classical Lévy processes and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment is established. The relationship with both microphysical models and experimental reali…
Algebraic quantum kinematics: Galilean covariance with positive energy confines unequal-time commutation to null sets
本文提出一个算子代数框架，将非相对论量子力学与狭义相对论联系起来，探讨了光子部分的实现、常数c和ħ的不同作用以及哈格-卡斯特勒网的结构障碍，提出了SR选择猜想。
We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has recently been developed [1,2]. We use the hyperplane formalism in order to perform a manifest covariant quantization and to implement initial correlations to the solution of the Liouville-von Neumann equation. A perturbative expansion in orders of the fine structure constant for the correlation functions as well as the statistical operator is applied. The non-eq…
We develop a covariant density matrix approach to kinetic theory of QED plasmas subjected into a strong external electromagnetic field. A canonical quantization of the system on space-like hyperplanes in Minkowski space and a covariant generalization of the Coulomb gauge is used. The condensate mode associated with the mean electromagnetic field is separated from the photon degrees of freedom by a time-dependent unitary transformation of both, the dynamical variables and the nonequilibrium statistical operator. Therefore even in the case of strong external fields a perturbative expansion in or…
The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (-1)^2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by mea…
Bell Nonlocality as a Covariance Obstruction in Locally Covariant Quantum Field Theory
本文揭示了局部协变量子场论中贝尔非局域性与协变性的根本矛盾，证明了在保持相对论因果性的同时无法嵌入经典因果框架的不可能性。
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^μintroduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within the identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed us…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as macroscopic constraints we consider statistical ensembles over the space of classical probability distributions or quantum wave-functions. The ensembles are covariantized using dual field theories with either complex or real scalar fields identified with complex wave-functions or square root of probabilities. We argue that a full space-time covariance on a field …
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