自旋-1粒子与自旋相关电势的拓扑研究

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"拓扑上大量的spin-1粒子和自旋相关电位" 本文是一篇理论物理学的研究论文，发表在《欧洲物理杂志C》(Eur.Phys.J.C)上，探讨了具有中间质量的spin-1玻色子在低动量传递时，如何影响铁电离子源之间的自旋相关的粒子间电势。研究由F.A.Gomes Ferreira、P.C.Malta、L.P.R.Ospedal和J.A.Helayël-Neto共同完成，发表于2015年。文章首先介绍了研究的背景和目的，即深入理解spin-1粒子（也称为介子）在特定场表示中的作用。Proca场是一种描述有质量的spin-1粒子的经典场理论，而在此文中，作者对比了Proca场与另一种由2型势与4矢量轨距场混合的spin-1玻色子。这种自旋1玻色子具有轨距不变的质量，这使得它在物理行为上与Proca场有所区别。在低动量传递的极限下，研究者分析了粒子间的电势，这些电势不仅依赖于粒子的自旋，还与它们的速度相关。通过对电势曲线的深入研究，他们揭示了这些自旋依赖的性质，这在量子力学和凝聚态物理中具有重要的意义。特别是，这种自旋相关电势可能对理解磁性材料、超导体和自旋电子器件等复杂系统的相互作用有重要贡献。在论文中，作者还讨论了这些理论结果可能的实际应用。例如，自旋相关电势可以用于设计新的自旋tronics设备，其中信息是通过电子的自旋状态而非其电荷来传输的。此外，他们还推导出了向量和伪张量耦合常数的乘积的上限，这是一个关键的理论限制，对于约束理论模型和未来实验的设计至关重要。这篇论文为理解和利用spin-1粒子的特性提供了一种新的视角，特别是在涉及自旋依赖相互作用的场景中。通过这种方式，科学家能够更准确地预测和控制粒子间的相互作用，这对于推动物理学的前沿研究以及开发新的技术应用具有深远的影响。

Eur. Phys. J. C (2015) 75:238

DOI 10.1140/epjc/s10052-015-3470-1

Regular Article - Theoretical Physics

Topologically massive spin-1 particles and spin-dependent

potentials

F. A. Gomes Ferreira

,P.C.Malta

, L. P. R. Ospedal

, J. A. Helayël-Neto

Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr Xavier Sigaud 150, Urca, Rio de Janeiro, CEP 22290-180, Brazil

Received: 28 April 2015 / Accepted: 19 May 2015 / Published online: 29 May 2015

Abstract We investigate the role played by particular ﬁeld

representations of an intermediate massive spin-1 boson

in the context of spin-dependent interparticle potentials

between fermionic sources in the limit of low momentum

transfer. The comparison between the well-known case of

the Proca ﬁeld and that of an exchanged spin-1 boson (with

gauge-invariant mass) described by a 2-form potential mixed

with a 4-vector gauge ﬁeld is established in order to pursue

an analysis of spin- as well as velocity-dependent proﬁles

of the interparticle potentials. We discuss possible applica-

tions and derive an upper bound on the product of vector and

pseudo-tensor coupling constants.

1 Introduction

Most macroscopic phenomena originate either from grav-

itational or electromagnetic interactions. There has been

some experimental effort over the past decades towards the

improvement of low-energy measurements of the inverse-

square law, with fairly good agreement between theory and

experiment [1,2]. The equivalence principle has also been

recently tested to search for a possible spin-gravity coupling

[3]. On the other hand, a number of scenarios beyond the

Standard Model (BSM) motivated by high-energy phenom-

ena predict very light, weakly interacting sub-eV particles

(WISPs) that could generate new long-range forces, such as

axions [4], SUSY-motivated particles [5] or paraphotons [6–

9].

The discovery of a new, though feeble, fundamental

force would represent a remarkable advance. Besides the

Coulomb-like “monopole–monopole” force, it is also pos-

e-mail: felipeagf@cbpf.br

e-mail: pcmalta@cbpf.br

e-mail: leoopr@cbpf.br

e-mail: helayel@cbpf.br

sible that spin- and velocity-dependent forces arise from

monopole–dipole and dipole–dipole (spin–spin) interac-

tions. Those types of behavior are closely related to two

important aspects of any interacting ﬁeld theory: matter–

mediator interaction vertices and the propagator of interme-

diate particles. The present paper is mainly concerned with

this issue and its consequences on the shape of the poten-

tial between two fermionic sources. This discussion is also

of relevance in connection with the study, for example, of

the quarkonium spectrum, for which spin-dependent terms

in the interaction potential may contribute considerable cor-

rections [10]. Other sources (systems) involving neutral and

charged particles, with or without spin, have been considered

by Holstein [11].

Propagators are read off from the quadratic part of a given

Lagrangean density and depend on intrinsic attributes of

the ﬁelds, such as their spin. Most of the literature is con-

cerned with spin-1 bosons in the





-representation of the

Lorentz group (e.g., photon). Here, we would like to address

the following questions: for two different ﬁelds represent-

ing the same sort of (on-shell) spin-1 particle, which role

does a particular representation play in the ﬁnal form of the

interaction? Is the form of the mass term (corresponding to

some speciﬁc mass-generation mechanism) determinant for

the macroscopic characterization of the interparticle poten-

tial?

The amplitude for the elastic scattering of two fermions is

sensitive to the fundamental, microscopic, properties of the

intermediate boson. Our work sets out to study the potential

generated by the exchange of two different classes of neutral

particles: a Proca (vector) boson and a rank-2 anti-symmetric

tensor, the Cremer and Scherk [13] and Kalb and Ramond

[12] ﬁeld, mixed to another vector boson, i.e., the



, B

νκ



system with a topological mixing term. Two-form gauge

ﬁelds are typical of off-shell SUGRA multiplets in four and

higher dimensions [14–18] and the motivation to take them

into consideration is twofold:

123

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