Locality in the Everett Interpretation of Quantum Field Theory

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest.     

Fermions without spinors

The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.     

Physics and Causation

The paper makes a case for there being causation in the form of causal properties or causal structures in the domain of fundamental physics. That case is built in the first place on an interpretation of quantum theory in terms of state reductions so that there really are both entangled states and classical properties, GRW being the most elaborate physical proposal for such an interpretation. I then argue that the interpretation that goes back to Everett can also be read in a causal manner, the splitting of the world being conceivable as a causal process. Finally, I mention that the way in which general relativity theory conceives the metrical field opens up the way for a causal conception of the metrical properties as well.     

Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973 [12]. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.     

无相互作用费米量子信道直积态容量研究

用费米线性光学方法,提出无相互作用费米量子信道物理模型.用平稳量子高斯态协方差矩阵性质及Majorization不等式理论,推导出在平稳高斯输入态下费米量子信道最小输出熵的表达式.利用在n模费米系统添加一个额外模的方法,得到平稳高斯态和高斯态输出熵的关系|利用此关系式,借助在高斯输入态下费米信道最小输出熵值是可达的猜测,推导出无相互作用费米信道直积态容量的表达式.最后,用最小输出熵的迭代算法验证已推出的费米信道最小输出熵表达式正确性,数值计算结果表明:对于带噪声的无相互作用费米量子信道,已推出最小输出熵与数值计算结果的吻合度可以达到10e-9.     

Fractionalization via Z(2) gauge fields at a cold-atom quantum Hall transition

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

轴对称黑洞的量子统计熵

避开了求解黑洞背景下波动方程的因难,应用量子统计方法,通过应用在量子引力中、由广义测不准关系得出的新态密度方程,直接求解轴对称Kerr黑洞背景下玻色场和费米场的配分函数.然后,在视界附近计算黑洞背景下玻色场和费米场的熵.得到用收敛级数表达的黑洞熵.在计算中不存在用brick wall模型计算黑洞熵时出现的发散项和小质量近似,使人们对非球对称时空中黑洞的统计熵有更深入的认识. 关键词： 量子统计 非球对称时空 广义测不准关系 黑洞熵     

New trends in density matrix renormalization

The density matrix renormalization group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond condensed matter, and is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and nuclear and high-energy physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview of the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite-temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the dynamical mean field method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.     

Causal signal transmission by quantum fields. III: Coherent response of fermions

Structural response properties of fermionic fields are investigated. In the presence of fermions the key technical concept becomes response combination, or R-normal product, of field operators. It generalises the notion of time-normal operator product to response problems. Time-normal products are a special case of R-normal products without inputs; this paper thus also generalises the concept of time-normal ordering to fermions. Explicit causality of R-normal products of arbitrary (bosonic and/or fermionic) field operators is proven, and explicit relations expressing them by conventional Green’s functions of quantum field theory are derived.     

Supersymmetry and bosonization in three dimensions

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.     

Particle Trajectories for Quantum Field Theory

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.     

Experimental simulation of the Unruh effect on an NMR quantum simulator

The Unruh effect is one of the most fundamental manifestations of the fact that the particle content of a field theory is observer dependent. However, there has been so far no experimental verification of this effect, as the associated temperatures lie far below any observable threshold. Recently, physical phenomena, which are of great experimental challenge, have been investigated by quantum simulations in various fields. Here we perform a proof-of-principle simulation of the evolution of fermionic modes under the Unruh effect with a nuclear magnetic resonance(NMR) quantum simulator. By the quantum simulator, we experimentally demonstrate the behavior of Unruh temperature with acceleration, and we further investigate the quantum correlations quantified by quantum discord between two fermionic modes as seen by two relatively accelerated observers. It is shown that the quantum correlations can be created by the Unruh effect from the classically correlated states. Our work may provide a promising way to explore the quantum physics of accelerated systems.