Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

If (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V ₁ and V ₂ are spacelike separated spacetime regions, then the system ( (V ₁ ), (V ₂ ), ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A (V ₁ ), B (V ₂ ) correlated in the normal state there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V ₁ and V ₂ and disjoint from both V ₁ and V ₂ , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( (V ₁ ), (V ₂ ), ) with a locally normal and locally faithful state and suitable bounded V ₁ and V ₂ satisfies the Weak Reichenbach's Common Cause Principle.     

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.     

量子场论中的自旋算符

从量子场论的角度对相对论粒子的运动自旋概念作了进一步深入研究.构造了场量子自旋以及场系统运动自旋两个新算符.给出了场量子自旋动量空间的显式表达式以及用Poincar啨群生成元表示的场系统运动自旋的显式表达式.借助这两个算符,可以干净地解决有关场自旋的问题,表明它们才是场自旋的恰当的算符.     

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.     

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.     

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.     

Quantum Field Theory and Dense Measurement

We show, using quantum field theory (QFT), that performing a large number of identical repetitions of the same measurement does not only preserve the initial state of the wave function (the Zeno effect), but also produces additional physicaleffects. We first discuss the Zeno effect in the framework of QFT, that is, as a quantum field phenomenon. We then derive it from QFT for the general case in which the initial and final states are different. We use perturbation theory and Feynman diagrams and refer to the measurement act as an external constraint upon the system that corresponds to the perturbative diagram that denotes this constraint. The basic physical entities dealt with in this work are not the conventional once-perfomed physical processes, but their n times repetition where n tends to infinity. We show that the presence of these repetitions entails the presence of additional excited state energies, and the absence of them entails the absence of these excited energies.     

Interference in Quantum Field Theory: Detecting Ghosts with Phases

This study discusses the implications of the principle of locality for interference in quantum field theory. As an example, it considers the interaction of two charges via a mediating quantum field and the resulting interference pattern in the Lorenz gauge. Using the Heisenberg picture, it is proposed that detecting relative phases or entanglement between two charges in an interference experiment is equivalent to accessing empirically the gauge degrees of freedom associated with the so-called ghost (scalar) modes of the field in the Lorenz gauge. These results imply that ghost modes are measurable and hence physically relevant, contrary to what is usually thought. They also raise interesting questions about the relation between the principle of locality and the principle of gauge-invariance. This analysis also applies to linearized quantum gravity in the harmonic gauge, and hence has implications for the recently proposed entanglement-based witnesses of non-classicality in gravity.     

Solomon’s Argument on Hidden Variables in Quantum Theory

J. Solomon [Journal de Physique 4, 34 (1933)] produced an argument of great generality claiming to demonstrate the impossibility of hidden variables in quantum theory, an argument which M. Jammer [The Philosophy of Quantum Mechanics(Wiley, New York, 1974)] said raised a number of questions. For the first time, this argument is discussed, a simple hidden variable model violating the argument is analysed in detail, and the error in the proof is located.     

Toward a Finite-Dimensional Formulation of Quantum Field Theory

Rules of quantization and equations of motion for a finite-dimensional formulation of quantum field theory are proposed which fulfill the following properties: (a) Both the rules of quantization and the equations of motion are covariant; (b) the equations of evolution are second order in derivatives and first order in derivatives of the spacetime coordinates; and (c) these rules of quantization and equations of motion lead to the usual (canonical) rules of quantization and the (Schrödinger) equation of motion of quantum mechanics in the particular case of mechanical systems. We also comment briefly on further steps to fully develop a satisfactory quantum field theory and the difficuties which may be encountered when doing so.     

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.     

Implications of Local Friendliness Violation for Quantum Causality

We provide a new formulation of the Local Friendliness no-go theorem of Bong et al. [Nat. Phys. 16, 1199 (2020)] from fundamental causal principles, providing another perspective on how it puts strictly stronger bounds on quantum reality than Bell’s theorem. In particular, quantum causal models have been proposed as a way to maintain a peaceful coexistence between quantum mechanics and relativistic causality while respecting Leibniz’s methodological principle. This works for Bell’s theorem but does not work for the Local Friendliness no-go theorem, which considers an extended Wigner’s Friend scenario. More radical conceptual renewal is required; we suggest that cleaving to Leibniz’s principle requires extending relativity to events themselves.     

Hyperfunction Quantum Field Theory: Localized Fields Without Localized Test Functions

This note addresses the problem of localization in quantum field theory; more specifically we contribute to the ongoing discussion about the most appropriate concept of localization which one should use in relativistic quantum field theory: through localized test functions or through the fields directly without localized test functions. In standard quantum field theory, i.e., in relativistic quantum field theory in terms of tempered distributions according to Gårding and Wightman, this is done through localized test functions. In hyperfunction quantum field theory (HFQFT), i.e., relativistic quantum field theory in terms of Fourier hyperfunctions this is done through the fields themselves. In support of the second approach we show here that it has a much wider range of applicability. It can even be applied to relativistic quantum field theories which do not admit compactly supported test functions at all. In our construction of explicit models we rely on basic results from the theory of quasi-analytic functions.     

光孤子约束系统的量子场论

光孤子系统可用奇异Lagrange量描述,系统含Dirac约束.通常按对应原理写出系统对易关系和量子运动方程时,未计及约束.文中对该系统进行严格的Dirac括号量子化,给出了系统的对易关系和量子运动方程,还对系统进行了路径积分量子化,并根据量子水平的Noether定理,导出了系统在时空平移变换不变性下的量子能量和动量守恒.系统还具有相位变换下的不变性,相应导出了系统的粒子数守恒.     

Free-Fall Non-Universality in Quantum Theory

The author shows by embodying the Einstein equivalence principle—local Poincaré invariance—and general covariance in quantum theory that wave-function spreading rules out the universality of free fall, that is, the free-fall trajectory of a quantum (test) particle depends on its internal properties. The author provides a quantitative estimate of the free-fall non-universality in terms of the Eötvös parameter, which turns out to be measurable in atom interferometry.     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.