Relativistic Nonlocal Quantum Field Theory

A theory is defined to be relativistic if its Hamiltonian, total momenta, and boost's generators satisfy commutation relations of the Poincaré group. Field theories with usual local interactions are known to be relativistic. A simple example of a relativistic nonlocal theory is found. However, it has divergences. Some conditions are obtained which are necessary in order that a nonlocal theory be relativistic and divergenceless.     

Field Theory Approaches to Relativistic Hydrodynamics

Just as non-relativistic fluids, oftentimes we find relativistic fluids in situations where random fluctuations cannot be ignored, with thermal and turbulent fluctuations being the most relevant examples. Because of the theory’s inherent nonlinearity, fluctuations induce deep and complex changes in the dynamics of the system. The Martin–Siggia–Rose technique is a powerful tool that allows us to translate the original hydrodynamic problem into a quantum field theory one, thus taking advantage of the progress in the treatment of quantum fields out of equilibrium. To demonstrate this technique, we shall consider the thermal fluctuations of the spin two modes of a relativistic fluid, in a theory where hydrodynamics is derived by taking moments of the Boltzmann equation under the relaxation time approximation.     

超核的相对论平均场计算

利用相对论平均场方法计算了奇异、粲和底超核的部分性质,包括各种不同味的超核的单粒子能量以及其他一些静态性质,并对结果进行了比较.对各种味的重子的势阱深度和耦合常数做了估计,得到丰富的结果.建议寻找质量数大于10?0的粲超核.同时探讨了不同重子杂质对原子核芯性质的可能影响.     

Relativistic Quantum Mechanics and Field Theory

The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality property and the gauge invariance encoded in the Gauss' law is discussed in connection with the various quantization choices for gauge fields.     

Finsler Geometry and Relativistic Field Theory

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of gauge transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.     

Remarks on Causality in Relativistic Quantum Field Theory

It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras (V ₁),(V ₂) associated with spacelike separated spacetime regions V ₁,V ₂ have a (Reichenbachian) common cause located in the union of the backward light cones of V ₁ and V ₂. Further comments on causality and independence in quantum field theory are made. Originally published in International Journal of Theoretical Physics, Vol. 44, No. 7, 2005,Due to a publishing error, authorship of the article was credited incorrectly. The corrected article is reprinted in its entirety here. The online version of the original article can be found at     

相对论平均场理论对Pb同位素位移的研究

运用变形的相对论平均场理论研究了Pb同位素链的基态性质. 对关联的处理采用了BCS方法, 不成对核子的处理运用了“阻塞”法. 计算的结果很好地符合了实验上Pb的平均结合能, 中子分离能, 同位素位移. 接着从原子核的微观结构出发, 比较详细地研究了Pb链同位素位移出现反常扭折这一重要性质的物理机制.     

相对论平均场理论中的有效超子-核子相互作用

利用相对论平均场理论,结合单超核的实验数据,研究了核介质中的Λ超子–核子有效相互作用.通过符合13ΛC超核中Λ超子1s轨道的结合能实验值,给出了5组Λ超子–核子有效相互作用参数.利用这些参数组对质量数从9到2?0?8的单Λ超核和核物质中最低Λ态的束缚能进行了系统计算,得到的结果与实验值相符.     

Wavelet Methods in Field Theory

We discuss the use of Daubechies wavelets in discretizing quantum field theories.     

Propagation of Relativistic Quantum Particles in Spacetime in Quantum Field Theory

The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.     

On Field Theory Methods in Singular Perturbation Theory

Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.     

Source Methods in Quantum Field Theory

Schwinger's source theory is used to present a pedagogical review of various methods and models in quantum field theory. In the interest of simplicity we start out with a charged scalar model. Later on we also incorporate more complicated concepts in order to treat quantum electrodynamics, effective Lagrangians and model approximations.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

RMF理论框架下用粒子数守恒方法处理对关联

在相对论平均场理论框架下,利用粒子数守恒方法处理对关联,给出了具体的理论公式和数值细节;并以24Ne为例,用该方法研究了它的基态和低激发态性质. Particle-number conserving method is adopted to treat the pairing correlations in the relativistic mean-field theory. The formalism and numerical techniques are presented. As an example, the ground state properties and low-lying excited states in~(24)Ne are studied.