Spin: The Classical to Quantum Connection

Non-relativistic proofs of the spin-statistics connection

A recent paper by Peshkin [1] has drawn attention again to the problem of understanding the spin statistics connection in non-relativistic quantum mechanics. Allen and Mondragon [2] has pointed out correctly some of the flaws in Peshkin's arguments which are based on the single valuedness under rotation of the wave functions of systems of identical particles. We examine carefully the claim that is made in the title of [2] that there can be ``no spin-statistics connection in non-relativistic quantum mechanics''. We show that we can derive the spin statistics connection for non-relativistic quan…

Reply to "No spin-statistics connection in nonrelativistic quantum mechanics"

In a previous paper [quant-ph/0207017] I gave an elementary proof, starting from stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles must be bosons. Since then it has been suggested that my proof assumed its conclusion, and that it is based on a theory "quite different from standard physics." [quant-ph/0304088] I show here that those two statements are incorrect.

弥合经典与量子神经网络之间的差距：残差连接

Bridge the Gap between Classical and Quantum Neural Networks with Residual Connections

本文提出混合量子残差网络，通过残差连接与量子态演化建立精确对应关系，实现经典权重到量子门的转换，并在混合态处理中利用量子关联提升分类性能。

On connection between classical and quantum mechanics

We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation. Heisenberg-Schrodinger non-relativistic quantum mechanics is considered adequate and complete. Since the suggested theory is dispersion free, linear superposition principle is not violated but cannot affect results of measurements due to spectral decomposition theorem for self-adjoint operators (the collapse of wave function).

利用量子电路建立自旋波经典描述与量子描述之间的联系

Connection Between Classical and Quantum Descriptions of Spin Waves Using Quantum Circuits

本研究提出一种表征自旋1/2粒子链上单自旋波的乘积态量子电路，解析验证其无界链极限下的正确色散关系，经模拟和量子处理器验证，为自旋波经典与量子描述的关联及量子处理器误差表征提供新思路。

Spin and Statistics in Galilean Covariant Field Theory

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.

Reply to "Non-relativistic proofs of the spin-statistics connection," by Shaji and Sudarshan

I earlier proved under stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles with no internal degrees of freedom must be bosons. Shaji and Sudarshan have criticized that proof, asserting that it is "based on single-valuedness under rotation of the wave functions of systems of identical particles." No such assumption was used. Here, to remove all doubt, I exclude the fermion possibility through a proof in which even the existence of rotation is not used. Following that, I assume that the Hilbert space is invariant under rotation to exclude other symmetries …

Relativistic Spin-Statistics Connection and Kaluza-Klein Space-Time

The non-relativistic formalism introduced by Berry and Robbins that naturally incorporates the spin-statistics connection is generalized relativistically. It is then extended to an arbitrary Kaluza-Klein space-time by a suitable generalization of the Schwinger treatment of angular momenta. This leads, in this approach, to the inclusion of the `internal' quantum numbers in the spin-statistics connection on an equal footing with spin.

Spin-Statistics connection and the gravity of the Universe: The Cosmic connection

I suggest that the Spin-Statistics connection is a consequence of the phase shifts on quantum scattering amplitudes due to the induced gravitomagnetic field of the whole Universe at critical density. This connection was recently brought out in the context of a new theory of relativity in flat space with matter, called Cosmic Relativity (gr-qc/0406023). This prediction of the correct gravitational phases is a consequence of any relativistic gravitation theory in the presence of the massive Universe. This can also be interpreted as related to the Mach's principle applied to quantum phenomena. Pe…

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field is mapped to a set of Yang-Mills gauge potentials and a complex scalar field. This result was previously proved for a Minkowski space-time using Fierz identities. As an ap…

Emerging Connections: Quantum and Classical Optics

Quantum optics and classical optics have coexisted for nearly a century as two distinct, self-consistent descriptions of light. What influences there were between the two domains all tended to go in one direction, as concepts from classical optics were incorporated into quantum theory's early development. But it's becoming increasingly clear that a significant quantum presence exists in classical territory-and, in particular, that the quintessential quantum attribute, entanglement, can be seen, studied and exploited in classical optics. This blurring of the classical-quantum boundary has opene…

Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator

The Dirac hydrogen atom with spin symmetry is shown has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type hydrogen atom is connected to a four-dimensional Dirac system with equal scalar and vector harmonic oscillator potential, by the Kustaanheimo-Stiefel transformation with a constraint.

Connection between closeness of classical orbits and the factorization of radial Schrödinger equation

It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schrödinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schrödinger equation. Some discussion was made about the factorization of a 1D Schrödinger equation.

Is there a dynamical cause of the spin-statistics connection?

Extant proofs of the spin-statistics connection (SSC) are kinematical. C S Unnikrishnan has suggested that a dynamical interaction leading to the SSC would involve spin and perforce gravity, the only known universal force. For the scattering of two identical particles, he considers [arXiv: gr-qc/0406043] the interaction of their spins with the gravito-magnetic field generated by their scattering motion through cosmic matter-energy. There the direct and particles-exchanged scattering amplitudes accumulate different quantum phases which provide the relevant bosonic/fermionic sign between them wi…

Berry phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material from a Classical Electromagnetics Perspective

The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical Schrödinger equation, writing both in Hamiltonian form. However, the aforementioned quantities are not necessarily quantum in nature, and for photonic systems they can be explained using only classical concepts. Here we provide a derivation and description of PTI quantities using classical Maxwell's equations, we demonstrate how an electromagnetic mode can acquire Berry p…

The fundamental connections between classical Hamiltonian mechanics, quantum mechanics and information entropy

We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while quantum systems can be considered the ones where the internal dynamics cannot be accessed at all. As information entropy can be used to characterize how much the state of the whole system identifies the state of its parts, classical systems can have arbitrarily small information entropy while quantum systems cannot. This provides insights that allow us to und…

On precanonical quantization of gravity in spin connection variables

The basics of precanonical quantization and its relation to the functional Schrödinger picture in QFT are briefly outlined. The approach is applied to quantization of Einstein's gravity in vielbein and spin connection variables and leads to a quantum dynamics described by the covariant Schrödinger equation for the transition amplitudes on the bundle of spin connection coefficients over the space-time, that yields a novel quantum description of space-time geometry. A toy model of precanonical quantum cosmology based on the example of flat FLRW universe is considered.

Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections

By requiring unambiguous symmetric quantization leading to the Dirac equation in a curved space, we obtain a special representation of the spin connections in terms of the Dirac gamma matrices and their space-time derivatives. We also require that squaring the equation give the Klein-Gordon equation in a curved space in its canonical from (without spinor components coupling and with no first order derivatives). These requirements result in matrix operator algebra for the Dirac gamma matrices that involves a universal curvature constant. We obtain exact solutions of the Dirac and Klein-Gordon e…

Disguised Electromagnetic Connections in Classical Electron Theory

In the first quarter of the 20th century, physicists were not aware of the existence of classical electromagnetic zero-point radiation nor of the importance of special relativity. Inclusion of these aspects allows classical electron theory to be extended beyond its 19th century successes. Here we review spherical electromagnetic radiation modes in a conducting-walled spherical cavity and connect these modes to classical electromagnetic zero-point radiation and to electromagnetic scale invariance. Then we turn to the scattering of radiation in classical electron theory within a simple approxima…

Parity as the foundation of the non-relativistic spin-statistics connection

It is shown that the symmetry under parity of the wavefunctions of two identical particles with an arbitrary spin $s$ in three spatial dimensions accounts for the appropriate wavefunction exchange statistics under the permutations of particles. The standard properties of the angular momentum in non-relativistic quantum mechanics account for the sign factor $(-1)^{2s}$ that the wavefunctions acquire under the permutation of coordinates of the two particles, without any additional requirements, directly relating spin and the particle exchange statistics in the non-relativistic context.

集体自旋-玻色子Lindbladian的无隙充分条件及其与耗散时间晶体的联系

Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals

该研究提出集体自旋-玻色子等系统Lindbladian主方程无隙激发的充分条件，揭示其与耗散时间晶体形成的关联，验证了平均场半经典方法的精确性。

On the Failure of Spin-Statistics Connection in Quantum Gravity

Many years ago Friedman and Sorkin [1] established the existence of certain topological solitonic excitations in quantum gravity called (topological) geons. Geons can have quantum numbers like charge and can be tensorial or spinorial having integer or half-odd integer spin. A striking result is that geons can violate the canonical spin-statistics connection [2,3]. Such violation induces novel physical effects at low energies. The latter will be small since the geon mass is expected to be of the order of Plank mass. Nevertheless, these effects are very striking and include CPT and causality vio…

经典弹性与量子复杂度的相遇：来自全息透镜的联系

Classical elasticity meets quantum complexity: A connection from the holographic lens

本研究探究全息非晶固体的剪切形变效应，发现剪切应力与形成复杂度随剪切应变增长且在超大剪切区遵循普适标度关系，还为大静态黑洞复杂度与贝肯斯坦-霍金熵线性标度的认知提供反例。