为了描述物理现实，场的动力学方程有两种构造方式：微分形式主义和积分形式主义。杨在规范场的情况下首先强调了这一事实的重要性[Phys. Rev. Lett. 33（1974）445]，这一事实引起了对Aharonov-Bohm相和磁势的更深入的理解[Phys.Rev.D. 12（1975）3845]。本文指出，这一事实在一般物质的波函数中也成立，从而加深对Berry相的理解。最重要的是，我们将证明一点，即对于物质的一般波函数，在绝热极限下，它的积分形式与微分形式之间存在着本质的区别。正是由于忽略了这一差异，导致了Marzlin和Sanders [Phys. Rev. Lett. 93（2004）160408]。用微分算子和积分算子构造场的动力学方程在物理上没有区别，这一点已被广泛接受。然而，我们的研究表明，薛定谔微分方程（即，波函数的微分形式）将导致Berry相位消失并且薛定谔积分方程（即，波函数的积分形式），在绝热极限下，可以满意地给出Berry相。由此得出结论：描述物理实在有两种方法，即微分形式主义和积分形式主义，但积分形式主义是唯一的完全描述方法。
英文摘要：
To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D. 12 (1975) 3845]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schrodinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrodinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience accumulated by classical lattice simulation and manifest Lorentz invariance. We discuss quantum computation of lattice gauge theory in the path integral formalism. We utilize a quantum sampling algorithm to generate gauge configurations, and demonstrate a benchmark test of $Z_2$ lattice gauge theory on a four-dimensional hypercube.
In this paper, I consider the issue of how two mathematical models of modern physics, the variational principles and the quantum path integral formalism, relate to reality. I assume that the observed phenomena are consistent with the calculations because both of these models have some common ontological foundations. According to the hypothesis of the summation of coexisting alternative possibilities, at the quantum level, the system at once moves along all histories that possible in given boundary conditions. The actual history is a mere result of the summation of all these alternative possibl…
Dissipative adaptation in a driven spin-boson model within the path-integral formalism
Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；Centro Brasileiro de Pesquisas Física（巴西物理研究中心）；Instituto de Física, Universidade Federal de Mato Grosso（马托格罗索联邦大学物理研究所）
With the use of the path integral formalism for finite-temperature field theory, I find the persisting vector and axial currents that are generated in quantum chiral fermionic systems. The role of the explicit violation of chiral symmetry by fermion mass is elucidated. For the case of quantum fermionic systems in the backround of an arbitrary smooth magnetic field, I show that the chiral magnetic effect is substantiated on equally the same footing as the chiral separation effect is. Both effects remain unaltered if chiral symmetry is violated by mass.
The Berezin--Simon (BS) quantization is a rigorous version of the ``operator formalism'' of quantization procedure. The goal of the paper is to present a rigorous real-time (not imaginary-time) path-integral formalism corresponding to the BS operator formalism of quantization; Here we consider the classical systems whose phase space $M$ is a (possibly non-compact) Kähler manifold which satisfies some conditions, with a Hamiltonian $H:M\rightarrow\mathbb{R}$. For technical reasons, we consider only the cases where $H$ is smooth and bounded. We use Güneysu's extended version of the Feynman--Kac …
We study boson-fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson-fermion duality between the Lieb-Liniger model and the Cheon-Shigehara model. We present an explicit construction of $n$-boson and $n$-fermion models which are dual to each other and characterized by $n-1$ distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boso…
Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation theory. Here we review the history, main features and present applications of the formalism. Our emphasis is on recent developments such as the path integral representation of open fermion lines, the description of colour using auxiliary worldline fields, incorporation of higher spin, and extension of the formalism to non-commutative space.
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset; (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto…
