A causal quantum theory in phase space

The causal theory for the coherent state representation of quantum mechanics is derived. The general conditions for the classical limit are given and it is shown that phase space classical mechanics can be obtained as a limit even for stationary states, in contrast to the de Broglie-Bohm quantum theory of motion.     

Nonstatistical quantum-classical correspondence in phase space

We study the properties of a causal quantum theory in phase space for which phase space classical mechanics is obtained as a limit. The causal quantum theory is obtained from a generalized coherent state representation. The behavior for the one particle case and the manyparticle case are illustrated for the harmonic oscillator. We also answer to the arguments against the possibility of constructing causal theories in phase space.     

薛定谔方程对单个粒子在均匀场中运动的因果描述

把薛定谔方程当成扩展了的经典力学中的雅科毕-哈密顿方程,对单个粒子在均匀场U(x)～±x中的运动进行因果描述。严格求解薛定谔方程,得到了上述两种情况下具有量子力学能级分立特性的粒子的速度随空间位置变化的曲线u(x),这两条速度曲线u(x)都可以遵循对应原理退化到与经典力学的速度曲线U_cla(x)重合。     

磁AB效应及其理论解释

本文介绍磁AB效应及其两种理论解释 ,进而说明经典电动力学具有局限性 ,量子力学是更高层次的物理理论     

Mathematical foundations of quantum field theory: Fermions,gauge fields,and supersymmetry part I: Lattice field theories

In this paper we explore the mathematical foundations of quantum field theory. From the mathematical point of view, quantum field theory involves several revolutions in structure just as severe as, if not more than, the revolutionary change involved in the move from classical to quantum mechanics. Ordinary quantum mechanics is based upon real-valued observables which are not all compatible. We will see that the proper mathematical understanding of Fermi fields involves a new concept of probability theory, the graded probability space. This new concept also yields new points of view concerning ergodic theorems in statistical mechanics.     

Electromagnetic and Force Field Equations

In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics.     

Functional methods in thermofield dynamics: A real-time perturbation theory for quantum statistical mechanics

A generating functional is constructed for real-time Green functions in quantum statistical mechanics in the context of thermofield dynamics. The KMS condition is taken as an axiom which together with field equations fixes the generating functional for causal Green functions in an interacting quantum field theory. This leads to Feynman rules for diagrammatic real-time perturbation theory.     

Quantum Mechanics Emerges from Information Theory Applied to Causal Horizons

It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde’s entropic gravity theory is also investigated.     

量子信息研究进展

量子信息论是经典信息论与量子力学相结合的新兴交叉学科。本文综述了量子信息领域的研究进展。即包括了为人们所熟知的量子通信与量子计算领域 ,也包括了刚刚兴起的但却有巨大潜力的量子对策论等领域。本文以介绍量子信息论的基本理论框架为主 ,同时也介绍了量子信息领域的实验研究进展。     

量子信息研究进展

量子信息论是经典信息论与量子力学相结合的新兴交叉学科,本综述了最子信息领域的研究进展。即包括了为人们所熟知的量子通信与量子计算领域,也包括了刚刚兴起的但却有巨大潜力的量子对策论等领域。本以介绍量子信息论的基本理论框架为主,同时也介绍了量子信息领域的实验研究进展。     

The renormalization group and the ϵ expansion

The modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory. The expansion in ? = 4?d is explained [d is the dimension of space (statistical mechanics) or space-time (quantum field theory)]. The emphasis is on principles, not particular applications. Sections 1–8 provide a self-contained introduction at a fairly elementary level to the statistical mechanical theory. No background is required except for some prior experience with diagrams. In particular, a diagrammatic approximation to an exact renormalization group equation is presented in sections 4 and 5; sections 6–8 include the approximate renormalization group recursion formula and the Feyman graph method for calculating exponents. Sections 10–13 go deeper into renormalization group theory (section 9 presents a calculation of anomalous dimensions). The equivalence of quantum field theory and classical statistical mechanics near the critical point is established in section 10; sections 11–13 concern problems common to both subjects. Specific field theoretic references assume some background in quantum field theory. An exact renormalization group equation is presented in section 11; sections 12 and 13 concern fundamental topological questions.     

Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse

The problem of the wave function collapse (a problem of measurement in quantum mechanics) is considered. It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation (annihilation) of a particle, an additional uncertainty arises, which "smears" the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term "collapse of the wave function" becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.     

Gauge invariance and gauge independence of the S-matrix in nonrelativistic quantum mechanics and relativistic quantum field theories

The gauge independence of transition rates as opposed to the gauge invariance of the equations of motion and gauge dependence of operators and state vectors is critically examined and explicitly demonstrated, both in nonrelativistic quantum mechanics and quantum field theory. Time independent as well as time dependent gauge transformations are explicitly analyzed using several techniques in order to clarify the physical content and significance of gauge independence and the conditions for its applicability.     

Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse

The problem of the wave function collapse(a problem of measurement in quantum mechanics) is considered.It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation(annihilation) of a particle,an additional uncertainty arises, which "smears" the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term "collapse of the wave function" becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.     

Deformation Quantization for Systems with Fermions

Deformation quantization, which achieves the passage from classical mechanics to quantum mechanics by the replacement of the pointwise multiplication of functions on phase space by the star product, is a powerful tool for treating systems involving bosonic degrees of freedom, both in quantum mechanics and in quantum field theory. In the present paper we show how these methods may be naturally extended to systems involving fermions. In particular we show how supersymmetric quantum mechanics can be formulated in this approach and consider examples involving both non-relativistic and relativistic systems.     

Independence in Operator Algebras

Various notions of independence of observables have been proposed within the algebraic framework of quantum field theory. We discuss relationships between these and the recently introduced notion of logical independence in a general operator-algebraic context. We show that C^*-independence implies an analogue of classical independence.     

Classical signal model for quantum channels

Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, the so-called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. We consider some consequences of the PCSFT for quantum information theory. They are based on our previous observation that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transforms of classical Gaussian signals.